you can make tabs visible to specific users… make your app public and then create as many tabs as you need… and set visibility to chosen users or whoever gets there first so they can have their own rooms… you can limit the amount of users in the rooms… and so on
The problem with the password option is that (as you’ve discovered) only one user can be signed in at a time.
My advice would be to make it Public with Email, and then Limit Access to emails in User Profiles.
The Free Plan allows up to 3 Private Users, so that should be fine for your use case.
You’ll just need to ensure that you have User Profiles correctly configured, and add a user profile row for each of the two people that need to use the app.
Actually, just looking again at your screen shot, that’s the old Privacy configuration. So once you choose the “Users in user profiles” option, that’s going to make your App private. But again, if you only want two people to be able to use it, that should be fine.