Mail stuck in "copying messages" - solved
About a week ago I got the problem where Mail is stuck in "Copying messages". Not only does this run the processor out of control, but it also means any changes you make in MacOS Mail are not reflected in Mail on your iOS devices.
Support's suggestions - reboot, update software, safe mode, try a new user account - do not have any impact, so it can be frustrating to debug.
Here is how I solved it. I have a lot of accounts that my MacOS Mail checks, mostly Gmail accounts and two iCloud accounts. Using Mail > Preferences > Accounts, I went through one by one, unchecking the "Enable this account" button then quitting and relaunching Mail, until it finally launched without the "Copying messages" status. This is how I identified which account was causing the problem. In this case, it was a Gmail account, and fortunately that account is thoroughly archived online.
Delete the account. Make sure you're actually deleting it and not just disabling it on this device. Then I re-added it, and everything was fine.
I hope this works for you too!
iMac 27″ 5K, macOS 10.15