h3o prateekmedia Thank you both for your replies and sorry for not reacting sooner, it turns out I hadn't properly configured notifications 😅 That's take care of now, hopefully.
I'm doing the Lock + Switch User dance, so that part I'm hopefully doing correctly. TBH, I wouldn't even expect Log Out not to terminate the session, so the behavior matches expectations there IMHO.
What I wasn't aware of is that there's a difference in Switch User behavior between regular users and administrators. Would anyone happen to know why that is? Is it a bug or a feature? If a bug, should it be reported somewhere, or has it been already (I'd like to subscribe to potential updates)?