please, please, please tell me some good 2 player games - give away added

I dont if this counts because its a mobile game but this game is pretty good
it has all the games you said
can be played with up to 4 players on the same phone

https://apps.apple.com/us/app/2-3-4-player-games/id1269516792
https://play.google.com/store/apps/details?id=com.ction.playergames&hl=en&gl=US

The Swords of Ditto is an excellent game to play with little ones. Same-screen co-op hack 'n' slash with great graphics and a good variety of enemies, with some (very) light RPG elements.

https://store.steampowered.com/app/619780/The_Swords_of_Ditto_Mormos_Curse/

It has been bundled before, so you might be able to find it cheaper in some forums versus buying on Steam.

https://store.steampowered.com/app/1331910/Morkredd/

Here are some games with shared/splitscreen which I reccomend:

Lara Croft and the_Guardian of Light
Lara Croft and the Temple of Osiris
Trine Enchanted Edition
Trine 2: Complete Story
Trine 3: The Artifacts of Power
Trine 4: The Nightmare Prince
How to Survive
How to Survive 2
Yooka-Laylee
Portal 2
The LEGO® NINJAGO® Movie Video Game
Splatter - Zombiecalypse Now

Broforce is a great game casual couch game. One of the best I have played.
These probably don't exactly match the genre your mentioned, but I highly recommend Overcook & Trine, but you did say "and more...".
I want to recommend "We Were Here" series for the puzzle category but I don't think it's possible to play it on the same machine.
I haven't played It Takes Two, but I think you can check that out as well. Same for A Way Out and Unravel Two.

The best coop game that I played nowadays was It takes two.

https://store.steampowered.com/app/249990/FORCED_Slightly_Better_Edition/

Basically a combination of a puzzle and beat em up game.
It was basically made for 2player coop. :)

cant think of any, but have a bump

Since I haven't seen it recommended yet, here is a personal favorite of mine and my brothers: https://store.steampowered.com/app/965680/Boomerang_Fu/

It's a great top-down brawler where you shoot boomerangs at each other and collect powerups to get the edge on your opponents. It's quick to learn, family friendly (if you need that), and is an absolute blast the more players you have.

bump! :)

https://store.steampowered.com/app/361300/Mother_Russia_Bleeds/
https://store.steampowered.com/app/985890/Streets_of_Rage_4/
https://store.steampowered.com/app/1287030/Bubble_Bobble_4_Friends_The_Barons_Workshop/

The LEGO games.
Carcassonne

From the games you have in your library I recommend LEGO NINJAGO.

https://store.steampowered.com/app/809870 this one is fun

I second all the lego games.
Furthermore
Serious Sam
Trine 2, Trine 4
Trackmania