Mac mini Mail.app intermittently stuck downloading Gmail

I have an M4 Pro Mac mini running 26.5.2, connecting to a single corporate Gmail account, and have been having an issue for months where Mail.app will intermittently take an unreasonable amount of time to download new messages. I've tried rebuilding indexes, reducing the amount of email on the server, updating the OS, and more; some fixes eventually get it working for a while, only for it to start flaking out again after a couple of weeks.

Similarly, if I just let it sit, after between tens of minutes and a few hours it'll suddenly kick in and start working normally, but as with any other fix it eventually comes back after a few days or weeks.

I am not having issues with this exact same account synced to my phone (Apple mail app, not the Gmail app), nor another Mac at home--just this machine, and it keeps coming back.

When it's in this stuck state, Mail is not doing anything: CPU use varies but is always in the low single digits at most, disk use is zero, network traffic also zero. It's just sitting there with a "Downloading Messages" status bar not moving.

More precisely in terms of symptoms, using today as an example: It was showing "Downloading Messages" and "8 of 12" for status. After no activity at all for 10 minutes, I did the following:

• Quit and re-opened Mail. No change, same Downloading 8 of 12 state after reopening.
• Rebooted. Downloading 8 of 12.
• Force-quit Mail and re-opened. Downloading 8 of 12.
• Installed the 26.5.2 update (on 26.5.1 before). Still Downloading 8 of 12.

I know from checking on another device that I actually had about 40 new messages, none of which had any attachments or were larger than a few KB. After maybe half an hour, it increased to 9 of 12 and added a recent message, then sat there for another 20 minutes.

Eventually, after maybe an hour of cumulative wait, it abruptly downloaded all new messages and started working normally again. New messages are being delivered immediately now.

The only thing that I can think of that is different about this install versus other Mail.app accessing the same account is that it has a fairly large number of local on-disk messages archived, but that's never caused problems before.

Any suggestions? It's driving me nuts.