I put in about 12 hours in a coop Gongsun Zan / Liu Bei campaign. In contrast to TW WH coop, you don’t start allied and can’t see each other’s moves. During battle you can observe (in which case the other coop player can gift units to you which you will control — same as previous TW coop), or you can control the AI troops.
Once we actually connected and were visually able to meet each other (which took more work than anticipated — both factions start in the North East, but there’s some hard slogging to get connected) — we were able to go the the diplomatic menu and negotiate. (Before meeting up, the other player wasn’t listed in the diplomatic menu.)
There was a diplomatic option to join forces and strive to jointly rule China together. From that point on, I think it’s same as previous coops. However, if you didn’t want to do that I believe you can just treat the other player same as other factions on the map — cooperate with them when you want to and fight them when you want to. Can’t say for sure what happens if you don’t join forces, we wanted to do the completely join in a permanent alliance option. So we went with that option as soon as it was available to us.
Until we actually joined up, I had no visibility on the other coop player and as far as the game UI was concerned, he didn’t exist. We ended up calling out province names and looking at the zoomed out map to try to get a sense of what the other player was doing in the fog of war. Plus we got to participate in each other’s battles even though we didn’t have any context on where said battles were taking place.
[Edit] one thing that is disappointing is that some of the character viewing options are disabled when the other player is playing. So you can see your characters, but can’t access the court and can’t check other characters relationships. So some of the stuff you might want to spend your time perusing during the other player’s turn in blocked. IIRC you can poke around your commanderies and look at building chains. You can also look over the tech tree and see the first page of the character sheets, just not the relationships part of the character sheets.