Try mastodon if you have not. Most servers are moderated way better and there are cooler people there anyway. :3
FoxFairline
Dorfromantik is a great one which was a big hit in Germany. Dunno if its widely known elsewhere but it should be, since it is a simple chilled coop Puzzler based on a cozy videogame.
The next two are not coop all the way but Mysterium and Treasure Island are pretty fun and invoke the same teamwork feeling around the table, if someone is content on beeing the GM.
In mysterium you have one person as a ghost, that sends visions to the other in form of abstract art cards, to find out how he died.
In the latter, one person plays Long John Silver and the other have to find his treasure on an Island (duh:), before he escapes prison and gets it himself.
It is meant to be played against each other, but if you tweak the rules a bit is very nice as a coop experience. Especially for kids, since you can draw on the whole map to mark down places that you rule out. Very nice family game for all ages.
I agree that most gamemodes do not play that way, and the classes are more restrictive to be a pure arena shooter.
But playing soldier or scout in gamemodes like Koth and PlayerDestruction scratch that itch enough for me to count.
Fast respawn and itemspawn management, combined with good map knowledge feels like good old quake 3 or UT sometimes.
Then you have dozens of rocketjumping maps in the server browser, which no game i know of has these days.
Guild wars 2! Giant map to explore and alright story in the free to play part.
Even if you pick different backrounds and race you can port to the other starting maps and the story connects everything later on.
It also gets more difficult so dont think it is always easy like in the starter zones.
And it is one of the old school f2ps thats still good without paying if you wanna try it out.
But if you spend money on an expac you keep it and dont have to pay for a savegame like WoW.
One of the rare MMOs that values your time and money.
If you want to scratch a similar itch, and have not already, try Guild Wars 2.
It does have microtransactions, but only because they have no subscription fee and they are mostly cosmetic with a few rare exceptions.
It also has no FOMO except cosmetics from certain festivals, which you can also buy in the next year.
It is still the best MMO on the market IMHO, because it values your time and money compared to other games in the genre.
(Better not) drop the bass!