Apple mail constantly downloading

An update to my situation for anyone who might have a similar problem someday:

I deactivated my gmail account in Apple Mail, then manually deleted all local mbox files and Mail preference and cache files in the Library. I then used google Takeout to download an archive of roughly half of my accumulated emails from gmail (the oldest stuff), then deleted those old emails from gmail permanently in order to reduce the total number of messages in the account. Then I imported the gmail mbox archive file into Apple Mail ("On My Mac," i.e. not associated with any account). Finally I reinstated my gmail account in Apple Mail and let everything re-sync. Now I have access to all of my emails in Apple Mail, and the weird syncing problems between Mail and gmail seem to have stopped.

I've had similar issues with Apple Mail in the past, and I think there must be a practical maximum number of message it can handle syncing from a server. I don't think the issue is a maximum in Apple Mail itself, since it seems to handle the large number of local emails just fine. My 2¢

A 2nd update for anyone who might care someday. Even after deleting half of my emails on the server, I started getting the same issues again after a few days. I resorted to limiting the IMAP mailbox size on the server side of things, and that seems to be working. It's irritating to have to go into gmail in my browser to do deep-dive searches, but it is what it is. We'll see if this solved it in the long term.

Ok, one more update. Sorry Apple mail, it's been great but we're breaking up. My gmail inbox and my apple mail inbox are not properly syncing at all, to the point that I'm not receiving some messages in my Apple Mail inbox, and a vendor went unpaid. God knows what else has been missed. Is anyone else having these issues with gmail, or is my account just bad?

...aaaand after all that, it's still having the problem. I feel like I'm about to say goodbye to Apple Mail. Help?