When the meeting starts, we’ll let people know

For starters, this is not a bug. Rather it's the Teams app that doesn't handle multi-accounts / multi-tenants particular well at this point. In general you should be signed in to Teams desktop and Outlook desktop with the same account to avoid issues. When clicking a meeting link and being signed in to Teams, you need to be signed in with the associated account/org. to which the invite was sent (or enter as anonymous guest not signed in). If not Teams is going to use the signed in account/org. credentials trying to access a meeting in which they weren't invited to, hence being stuck in the lobby as not being recognized (that is if not "everyone" is allowed).

So this is a combination of using the Lobby options as an organizer and which tenant you're currently signed in to.

Using InPrivate / Incognito browser sessions is an alternative if having issues with the app.

Choose who can bypass the lobby

Change participant settings for a Teams meeting (microsoft.com)

For a deep dive Meeting Lobby Behavior in Microsoft Teams : Jeff Schertz's Blog