Here’s some great cooperative games that either have big groups working together OR have the whole groups:
Escape from the Dark Castle - a fun little dungeon crawler where you flip cards and roll against dangers as you try to overcome obstacles. Completely cooperative but mechanically simple.
Wavelength - the base way to play is technically a ‘competitive’ in that there are teams and points but it’s relatively chill and I’ve often played this at parties with large groups cooperatively cause it just makes for a great conversation starter.
Phantom Ink - two teams but the mechanics are very fun and the game overall has a great tone.
Ravine - cooperative game where you try to survive after a plane crash.
I would also maybe recommend looking into some light roleplaying games like The Zone or Fiasco. These are almost always gm-less or easy to run and focused on building a fun narrative together.