Would a collection of group chats (not even necessarily all on the same service) be an example of the sort of thing you're thinking of? Each chat is small and contains people who directly know one another; but each person may be on any number of different chats. Information only leaks from one to another if someone explicitly forwards it, not by algorithmic recommendation.
I think in real life most people have multiple roles, for example if you are a parent and a software developer, you talk to other parents about parenting, and to other software developers about software development, but you usually don't ask random parents for programming advice or random software developers for parenting advice. This can be modeled by people talking in different chats (like in Discord), instead of having a "friend or not friend" binary (like in Facebook or Twitter). In reality, there happens to be some overlap, like I may have a friend with whom I discuss both parenting and programming, but usually I have different friends for different roles.
Then there are also roles like "my relatives" and "my neighbors". This gets tricky, because these are not completely transitive, like someone who lives on the next street is my neighbor, but someone who lives hundred streets away is not? Similarly, a cousin of my cousin is almost a stranger to me. This is probably better modeled with the Facebook-like approach, where I connect to my cousin, he connects to his cousin, but I am not connected to the cousin's cousin? But it would still be better if the software specified the role of the connection, such as "relative" or "neighbor" instead of just a generic "friend".
We also have a concept of private and public setting, like when I am speaking at a software developers' conference, it is public speech, and when it's four neighbors drinking in a pub, it is private speech. I guess the difference is something like "does everyone know everyone else in person? or can any stranger join?". In public setting, there are the speakers and the audience; the organizer is responsible for the speakers but not for the audience, the speakers are one who talk freely, and the audience may be invited to comment but may also be silenced.
I am currently finishing a PhD in network physics and have been thinking about this exact topic for a while. It seems reasonable to me that the way we handle inter-individual cooperation is cognitively limited in some way by the Dunbar number. Moreover, some other topological constraints could also occur. In their 1998 milestone paper (https://www.nature.com/articles/30918), Watts and Strogatz basically explained that in a multi-player Prisoner’s Dilemma, the higher the number of shortcuts, the less likely the emergence of cooperation. These shortcuts are randomly connected "long-range" edges, differing from the regular "friend-of-friend" edges. Such long-range edges are omnipresent in online social networks.
I think it could be highly beneficial for society to get used to defining the processes where human-scale mechanisms are "overwhelmed", leading to strong biases and unexpected behaviors. Online social life, I believe, is one of the most prominent examples of this phenomenon.
Short post and I don't have the math background to go into this more rigorously, but just going based off intuition.
Media platforms that create a single giant graph with tons of nodes and edges give rise to emergent dynamics that humans did not evolve to deal with. The worst voices get elevated, polarization increases, and we get phenomena like memes and virality. I think these create misaligned incentivizes.
Humans do best in strongly connected networks of up to a few hundred. The networks are then loosely connected to each other. There is high trust within each cluster because everyone knows everyone, which significantly reduces the risk of polarization, and also moderates the most extreme voices and egregious behaviors. Members of different clusters can interact with other clusters, but not arbitrarily: there is a time and protocol for doing so.
This is how tribes, villages, and towns interacted with each other for thousands of years - not one massive public square. I think a digital network organized like this would be much healthier than modern social networks.