Mail problems

I've been afraid to update to Big Sur because I'm having serious email problems with Catalina 10.15.7 on my iMac, and I read online that Big Sur has email problems as well. What's happening is that the emails in Mail are no longer stable--messages disappear and then reappear all day long; flagged messages head down to zero and then back up again. This seems to happen mostly but not exclusively with gmail. I spent many hours on the phone with an Apple support guy who was sure he had fixed it, but it's back worse than ever. Mail seems to be continually downloading messages (that's what it says at the bottom of the left-hand frame). The tech guy limited the number of messages being downloaded on gmail to 10,000, but that didn't do anything. I never had ANY problems with Apple Mail before this fall. Anybody have any idea a) what's going on, and b) how to fix it?