Welcome to this forum Sirius, you are a social coder now and part of the movement! 
Donât worry about naive. There is no such thing, Your post is spot on and in the most useful language: people talk, not tech talk which comes later. Besides, most naive posts likely already mine where they seem utopian and I claim they are not. 
âCommon groundâ is a great name, and as students you are uniquely positioned to bootstrap initiatives like these. It is easier to have ârunwayâ as a team next to the obligations the studies impose. My own focus is on the Commons, and in wordplay I use that, and might say âcommons groundâ in this case. Iâve experienced first-hand how hard it is to have the technology base be commons-owned, so that what is built upon it is not the same pile of junk that is supposed to keep society running (aka hypercapitalism in my vocabulary).
I think we all agree on the âasapâ in that sentence. The question is âasap, what?â. Thereâs good news, good news, and bad news. The good news is that the technology in theory is all there, patiently waiting to become useful innovation. The good news is also that today you can build a platform based on your new insights, and it may become a success. The bad news is that if you want to serve the commons at scale in a way that creates societal impact, the technology is NOT there and wonât be for a couple of years minimum.
Some other good news to the bad news is that that is your opportunity area, as you will need years to develop something that can have societal impact. Especially if you donât want to see that become just another extension of the corporate web, where hypercapitalism festers better than never before. As students I think you are more aware of ethics and the need to address externalities, less need to see this meme I posted to the fedi:
If you want my opinion.. currently we are building Skynet, because we donât know any other way to build humane technology within a commons. We think however that we are NOT building Skynet.
Aside: The âfediâ abbreviation is a petname for a âsegmentâ of fediverse bounded off by its cultural values. A culture with similarities to what existed in the days of the early Web. It is a precious culture, and it is disappearing/watered down by a kind of Eternal September introduction of newcomes fleeing big tech platforms. It is also a difficult culture, that in many ways is a social minefield where you better walk on eggshells. It is âsocial Wild Westâ, which is much better than social wasteland of tradtional corporate social media.
You are in the areas of communication, so I need not tell the importance of language and terminology. Iâd immediately drop ânew social mediumâ as a concept. We donât need new mediums. Mediums just indicate channels, and we have enough of them. We need to understand how to use them less poorly.
Thereâs a very interesting job here for skilled communicators to help the techies increase the âsocial bandwidthâ on these thin copper and glassfibre wires. It has taken me quite some time to appreciate how much mankind underestimates the impact of technology and takes it for granted when its ditched into society. I guess this must be especially true in Western cultures, where tech is seen as progress and âleading the wayâ.
To become experts in developing a common(s) language I advise you to delve into âStrategic Designâ, which is a comprehensive totally non-technical part of Domain Driven Design (DDD). And donât get lost in other parts of DDD (web search delivers you a tangled mess here). You might also want to look into event modeling or other methods built on top of DDD practices. At minimum develop a Ubiquitous language (UL). This becomes your âhandshakeâ to the tech world as well, and will avoid tons of misunderstanding and waste.
Instead of âsocial mediaâ consider using âsocial networkingâ and realize this is nothing new and what people do for thousands of years. Now we do it online, and somehow we think that thatâs business-as-usual, and we just have an âextra lineâ. Tremendous waste and parasocial communication we take for granted.. we hardly perceive them as we accept many things as normal. Making simple analogies to offline social practices is a great way to point out the weirdness in our online behaviors.
Other terminology advice: Avoid âappâ, âuserâ, âplatformâ in your ubiquitous language. They lead to dogma and bias, stuck innovation, and Conwayâs Law more-of-the-same end results. Only use these terms where they make sense to the particular domain you are considering.
TLDR is there a niche for what you want to do? Oh my god, thereâs a chasm. And here at social coding movement you are at the right address. Before you lies an unexplored field of IT: Social experience design.. where social meets the technoverse.
This is what I call âresidential social networkingâ, a subject area that I pursue for a decade now along with my crazy techno-philosophical background research (âprofessional hobbyismâ only, a mere dream, I wonât bore you with it but it involves investigating how an alternative to hypercapitalism may be introduced successfully into society). I have very particular and unorthodox ideas in this area, which are however waiting patiently in the attic of my brain, as both the technology base and the means to control it responsibly are not there yet atm.
In terms of current initiatives I would encourage to contact @ivanminutillo and @mayel of Bonfire Networks who are likely furthest on the Fediverse in thinking in same directions as you are with Paranova.
Another research initiative (that is I think dormant right now) to check is openEngiadina. Then the Lemmy developers are creating a federated wiki called Ibis. I should definitely cross-ref Semmy too here, an idea parked at the movement and ready for ideation to commence on it.
This entire subject area is encompassed by my new applied research area (as âprofessional hobbyistâ mind you, certainly not as academic expert) of hedonic commons-based peer production in grassroots environments.
Iâll cross-ref the diagram from https://discuss.coding.social/t/proposal-start-a-fellowship-to-explore-the-social-web/571 for that. And Iâll immediate add that you should consider your initiative to be candidate for the fellowship, so give the proposal topic a peek if you wish.
(It needs some updates, SOS â SOSS, Sustainable open social software, plus Fediverse and Open social stack shouldnât acronym FOSS.. that was a tease to make a point about FOSS general unsustainability)
Congrats, you have found entrance to a huge tech ecosystem that is in dire need of more science to turn into furtile innovation that progresses mankind, and to address this transfer systematically so it becomes sustained and sustainable. 
This bridging is very much topical to social coding movement. This forum likely works best for elaborating on a broad range of applied research. Big part of SX is focused on the (co)creation processes and supply chains that support intricate social experiences.
(Btw, part of the movement is Delightful Club and I co-curate delightful-open-science. All credit for current list goes to Victor Venema. We both lack time to maintain the list, so if any of you want to co-maintain: post to the chatroom or to #ecosystem:delightful category and I can hook you up.)
If my crazy techno-philosophical quest has learned me anything, then that is that âSimple solutions still existâ. My decade of dreamwalking has given me some you might say profound insights. I hope maybe I can unfold some of that into material reality. But the dream itself was worthwhile and useful, a source for gaining life exerience, strange as that sounds.
I am convinced that when it comes to simplicity and simple solutions, that can nonetheless carry the weight of society, then mimicry of nature and natural laws is the only way to go. Should we be able to unravel what sparks the commons into furtile collaboration at scale, we can unleash unstoppable forces for good.
Thatâs utopic, until it is not. And it depends on the number of minds and souls who proactively dedicate to pursue - what seem to be mere - dreams. Dreams are where passion and intrinsic motivation come from. They are drivers of life.
In the light of mimicry of nature it becomes clear that âcontent moderationâ is an artificial construct. Other than for very specific use case where it might be useful, it is needed solely by the inadequacy of our social web where âsocialâ is just branding invented once by marketeering techbroâs. Not the real deal. Remember that well, because that is the huge niche or chasm to take position in, imho.
A new huge area of things to discuss here. Hereâs question how your initiiative best position itself. Whatâs ambition level, the mission / vision / purpose questions, roadmap and evolution, breadth and scope. Lotta considerations.
Holistic sustainability and sustainability-first approaches are also study topics of social coding movement, because only Sustainable open social systems & software (SOSS) can reliably be adopted broadly in the Open social stack (the techstack / technosphere + social / solution layers). See on this forum the subject of #sx:fsdl
I know in academic realms all is not well in terms scientific practices and commercial influences that promote a wrong system of incentives (it promotes vices, which are big drivers of hypercapitalism). I donât know the extent to which your group of students is exposed to that. In your spare time, picking up this initiative you are liberated to apply actual fundamental science and go the fullest on realizing actual innovation. Maybe you arenât aware how little actual innovation comes from the business sector and Big Tech, esp. given all those billions of dollars they have to their disposal to innovate. Innovation simply isnât their goal, domination is. Status and power, a shallow game, that victimises humanity. I need not explain more. You indicated all that in your intro.
Just wanna mention: There is a big lure to get your own business going, and monetize, find business models. Here you can quickly stray, and become (or stay) part of the wicked problems that mankind faces. Seek (holistically) sustainable business and donât be afraid to apply the utmost of your fantasy, imagination and creativity in moving forward. Dare to be naive and it will lead to refreshing insights. 
You can go the route where you prototype, find techie companions in your team, build community, and then a MVP, Minimum viable product of your social networking concept. Yet there may be more value if you orient more broadly on how to connect YOUR particular studies to this whole outline I am depicting. Thatâs the first entry point to the âgold mineâ of life experience and different pathways of passion that match your individual dreams. It is also - to speak in more concrete terms - the best way to consider the entire âvalue portfolioâ you might develop.
This is great. How you have most chances, if you keep that spirit. I mentioned dreams.. they avoid disillisionment in case you foster impossible âvisionâ. Avoid visions, just dream and adjust them when needed. Or dream another dream. It is more casual and keeps you open-minded, away from dogma.
I will conclude my very long response, which your topic warranted, hauling back to the good news, good news and bad news I started with. The bad news is solved with patience, proactive participation and on to hedonic peer production and an open social stack where we can weave social experiences into the existing social fabric so that supportive humane technology might help choreograph human interactions more effectively and efficiently.
Simple solutions still exist .. ?? 