The only way to access a gitlab.com repository from Sourcetree is to add PAT authentication for the account. If you have a second repo that is accessed with a different login, you can add that login and PAT, but it will DISABLE access to the first repo even though the authentication manager shows a green checkmark for both accounts. Then the only way to again access the first repo is to refresh the PAT, which again disables access to the second repo...
...and on and on until you just buy a second computer for the other account, but one day you really really REALLY need to access the other repo from that computer...it's basically life or death...and the PAT you saved (like, why would you save it at all if it wasn't for this problem?) is saved on the other computer, so you just create another PAT and you start naming them really passive-aggressively to show your frustration even though nobody will ever see it...