Dear Natalie Shade,
Good day!! Thanks for posting your concern in this Microsoft Community.
Per the description shared, I would like to summarize your concern i.e., @ mention feature is not working as expected in the PowerPoint application on Mac, where it’s asking you to sign-in and no success when signing out, and signing in back.
If my understanding is correct, I would like to suggest you remove the Office apps activation using the removal tool. Reference: How to remove Office license files on a Mac - Microsoft Support
After it’s done, restart your Mac> Open your Outlook app and setup your account> After successful setup, open your PowerPoint app and check the outcome.
If the problem persists, can you please provide the version of the PowerPoint app? Open the PowerPoint app> Click on the PowerPoint in the Menu bar> About PowerPoint.
Thanks for your patience and understanding. Have a good day!!
Sincerely,
Mia | Microsoft Moderator