One screen, split in two
Split-screen is having a quiet renaissance, and it's the best format for two people who want a single, shared story. The screen divides, you each control a character, and the whole game is built around the two of you working together. Several of these even keep the split-screen when you play online, so you get the same design whether you're side by side or apart.
Our top split-screen pick is It Takes Two- every mechanic is designed for two, it's split-screen the entire way, and the Friend's Pass lets a second player join free. Its follow-up, Split Fiction, adds crossplay. A Way Out is the earlier two-player prison-break, Portal 2 is the best-value split-screen puzzle game, and Borderlands 3 brings split-screen to a four-player looter.
One thing to check: most of these are two-player stories. If you have a bigger group in the room, the couch co-op page lists 4-player local picks. If your second player is remote, confirm the game supports online co-op (It Takes Two and Split Fiction do) and check the crossplay hub for platform mixing.