It's a complex situation and I'm tired, so I'll try to sum it up:
I struggle with depression/anxiety and feelings of isolation, and at this point only regularly get social interaction seeing my best friend once a week. He has a separate friend group from me made up of several people that he sees weekly as well, who he plays tabletop games with n stuff. He's had this group for many years, since highschool, and I've met and hung out with them a handful of times. We get along quite well!
I've lowkey been trying to become a regular part of that group for years now, but have recently intensified efforts to join due to my mental health worsening. I stopped beating around the bush and let him know about these feelings out loud a few months ago when I had a mini nervous breakdown of sorts, but things overall haven't really changed since. He didn't react the way I needed him to in the heat of the moment, which was disheartening to me, but that weekend he invited me to hang with the group since they were coincidentally having a non-tabletop hangout that week, and it did wonders for my mental health. Problem is: It's now been several months, and at this rate I'm on the road to another breakdown if nothing bigger changes. His main "excuse" why I can't do tabletop with them is that the group's too full. And when I suggested me just watching and not playing so I could still hang, since being around a friendly group is ultimately what matters to me, apparently that would still be an issue because "having a spectator would mess with the vibe".
I'm afraid to ever bring it up because I think broaching the topic annoys him, and like I said, he's basically the only life preserver my mental stability has this point, so I'm terrified of accidentally pushing him away.
We're both autistic also btw, and in different ways I think. He specifically seems to have more difficulty with empathy than I do.
He's a good guy, and I love him, but I am just so deeply, deeply frustrated.
Have you considered inviting them all to do something with you? Movie night, bar trivia, playing a boardgame you want to try, etc. If you want to hang out with them, then come up with a reason and make it easy for them. You're going to have to do the emotional labor, but it sounds like it would be worthwhile if it helps your mental health. If your friend is being cagey about it then there might be something more going on, but it sounds like you should just be up front and say that you like these people, you'd like to spend time with them, and you're willing to put in the effort to make it fun.
Don't press the issue of the tabletop game. TTRPG groups are a delicate balance and they really only work with max 5-6 people in the room. Your friend is being honest with you when they say there isn't room, that's just the reality of the hobby.
This is a delicate social situation so I don't really have any advice, but just wanted to say that sucks and you have my sympathy =(
As an autistic GM, groups being too full is kind of a legitimate complaint. I find it's a clusterfuck including everyone's respective strengths above four players, with five as my personal hard cap.
Do they ever do other activities together?
Can you be direct in asking that you need human contact and if he can include you in social activities that aren't necessarily the aformentioned TTRPG?
Brring it up again and ask what his hesitation is about. If this is really your best friend he should tell you. I think he probably just wants to keep two aspects of his life separate but you need to let him know, again, that you need this
Be direct, you know he's dodging the situation.
Also autistic, so don't trust me too much on this, but maybe try something like a group chat with them first? Then you can either patiently wait for one of the friends to invite you to something or drop hints or straight up ask if anyone wants to hang out. If you wanna get wild, do it when your best friend is busy with something else.
Idk, I'm not good at having friends so I feel like my advice is probably bad here if you want to maintain your relationship with your best friend, but if the other people want to be your friend and you want to be their friend, your best friend should help that happen, not prevent it
Edit: hell, even if they don't want to be your friend he should help you anyway. Honestly I'm getting kinda mad at your friend rn