Thanks for jumping in on this discussion. It appears that many of these threads with questions go unanswered. I have also posted this question to the team at Workplace. Its clear that Workplace is the director service and front end for the Workrooms scheduling and configuration website. Actually the same GUI. I would expect that the Workplace team has encountered this issue or is aware of it.
Yep, this is pretty bad. I saw your other post about it requiring a separate login and that's where I ended up as well after opening a support ticket with Workplace and the answer from there being they don't support Workroom.
This is a pretty bad way to manage logins (or in the case of the private ones, completely unmanageable) and really needs to be addressed by Facebook/Meta.