Games which do not end friendships, but strengthen them.
I can answer this part of your post with:
- Slay the Spire The Boardgame (4p vs env)
- Sky Team (2p vs env)
- Bullet❤️ (1-4p vs 1 npc)
- Aeon's End (1-4p vs 1 npc)
- Between Two Cities (Co-op between players to your left and right but still competing with each other and the other players)
Games where working together works and loners fall behind.
This qualifier is a bit harder to answer, I'll have to think and look through the TT games I've played