Aw, you remind me I used to share Pokémon Colosseum/XD with my cousin by splitting the team: three Pokémon for him, three for me
Each one had full control of which Pokémon to use and what moves to give them, and since the games had almost every battle be a double one, we'd have one Pokémon from each "personal team" on the field at all time and we'd take turns with the controller to choose what our next move would be.
Nowadays I don't have friends in the physical world who I could invite to my house to do this, or a more chill "one plays and we comment on it" approach like you mention

My bf sometimes streams what he plays (Hollow Knight, Dark Souls...) and I look at it and we have some casual chat, I ask him things about the games, we make jokes and help with advice on segments

Recently we did something similar but with games we haven't played yet, that's how we ended up "couch streaming" Hypnagogia and Baba is You, among many other smaller indie games.
For a game to play with friends this way, either in person or online, I recommend The Sims. That's another game I streamed for my bf and it was fun when I was figuring out the game and trying and failing to make my Sims kiss

I think games that easily lend themselves to chaos (Sims, GTA, Palworld, Minecraft...) are great for this. Even if many of these have integrated multiplayer, I really like setting things on fire, building questionable things, or setting
myself on fire