Would both people always have to be playing at the same time? Or would it be possible for one person to play and progress while the other person isn’t playing?

I think you could go either way. If you want to be able to play without the other person also playing, you'd need a server or someone/something hosting the "game" where you connect in. If you were really clever as a programmer, you may be able to sync actions after both people are online without having a server, but that would be a challenge.

The other option is something like couch multiplayer, where you're both playing on the same device. If one person isn't there to move around, then no biggie.

I think the idea of an open world RPG with more than one player, not necessarily competitive or coop, but each with their own quests and motives, is interesting. I’m often hanging out in discord with friends, and we’re all just chatting while playing different games. We might as well be playing in the same world, and occasionally influence each other.

Me too! One thing I'm looking at trying out soon is the multiplayer mod to Elden Ring. It's enables a mechanic that's very similar to this goal, but not entirely.

In an open world where just a few people are playing their own game, together, you could have very fun friend interactions like trading and helping with quests or missions.

You’d have to somehow make it clear to the players that the goal is not to party up and just walk around doing everyone’s quests together, though. Ooo what if it was the world of the last airbender, and each person started as a different bender in a different part of the world? And maybe one person is secretly the avatar, but they don’t know until they’ve progressed. Ok, I’ll stop intruding on your idea lol.

Right -- I imagine when you both start the game you both get a very different intro, and are clearly starting in different parts of the world. I don't know much Airbender lore, but that sounds like a great theme for a game like this.

One feature I'd like to see is the two players' stories intertwine in such a way that you absolutely do have to help/meet to beat the game. Like, one player is arrested in jail and the other has to help them break out, because the one in jail is the one that can get the one not in jail access to the dungeon/castle/area that he wants to go to. Ultimately, I think it'd be important to kill the final boss/end the game together.