It's something about their federation tech vs google. Google, if you are in wrong service, nice switch account, one redirect it feels like.
It really does feel like something is broken on the back end of Microsoft's SSO, but I'm sure it's just so complicated with decades of cruft that it's hard to dig out.
It's seriously bemusing to be logging in to an organisational account with admin access only via a personal Gmail account username but there's literally no migration path for these early adopter accounts.
As far as I can tell, the easiest way to switch users is to go to https://www.office.com/login?es=Click directly (?es=Click is important) which will present you with all the accounts you're 'Signed in' with, even if office.com has you locked into one. Then you can use the app switcher to switch domains, which ensures the correct account.
I never access any email ever from a browser - Outlook is unbelievably good, and with the .PST file size restrictions no longer being restrictions I have my entire email archive of ever in it. Been doing things like this since 2002.
¹ Social media is the exception. Where I have multiple social media accounts (Instagram) I use seperate browsers (Edge for hobby account, Firefox for personal account). This is not ideal but the workflow is easy.
It is a great mistake login in on different accounts on the same computer ...