When I delete large numbers of e-mails on "Inbox" and move them to "Trash" they immediately pop back up into "Inbox."

Try rebuilding the affected Mailbox: Rebuild mailboxes in Mail on Mac - Apple Support.

You can rebuild any Mailbox including Inbox, Trash, Sent, etc. I recommend rebuilding all of them.

This happened to me up until a couple of months ago. If you selected a few (17 messages or so) and then delete them they would disappear. Today I can select all Trash/Junk and delete in one click of Delete to empty.

Is your Big Sur macOS up to date?

Mike Noonan

So far I've noticed this seems to apply when selecting batches across multiple senders. Single senders seems to work.....