I know many people with mental health issues (including myself), but my sample isn't terribly generalizable as they're either from my family or my wife's family

I know many people with mental health issues (including myself), but my sample isn't terribly generalizable as they're either from my family or my wife's family. For me personally, the scenarios I've opened up in are, without exception, intimate. The absolute maximum has probably been 5 people in conversation, and it has always been in scenarios where time feels plentiful. It also helps tremendously if others break the ice, though that's not always a requirement. For these volunteers that are trying to improve the mood of those struggling with no prior credibility or relationship, my best guess would have been organizing something like a series of cafes where people can come and pet consenting animals. Have volunteers be available for conversation, but defer agency in that process to participants. I would consider things like have a rotation of volunteers semi-clandestinely engage in alone time with the animals so that socially anxious participants don't feel overly conspicuous if they also need to be alone. I might also have some PPE on-hand for those especially anxious about hygiene. I'd probably look a bunch of stuff up to see what accommodations are helpful to people of various mental struggles, figure out a subset that seems plausible and give it a shot. That's my best guess.