Hello lhfrank,
Thanks for reaching out in Apple Support Communities. We understand that you're having trouble with your emails. It looks like the emails disappear and they appear in "All Inboxes." We're happy to help. For this particular issue, we'd like to see if the issue is replicated in safe mode. Safe mode prevents your Mac from loading certain software as it starts up, including login items, system extensions not required by macOS. If your Mac fully updated with the latest version of macOS Big Sur? Staying up to date helps ensure your device can function the best. In case you need to update your Mac, back up your Mac to secure your data.
Check out the following support articles:
How to use safe mode on your Mac
Back up your Mac
How to update the software on your Mac
Cheers!