I have copies of my Fastmail mail on several computers and access the mailboxes when online or offline. It syncs perfectly, is backed up through normal backup techniques and I am in control. There is no mystery here.

but wouldn't that just depend on your mail client?

its technically possible to edit the mail body on the server side and serve the modified message under the same mail ID.

I'd wager most clients would invalidate their local copy and trust the new mail from the server, but have to admit that I've never tested such a scenario.

iOS and Apple mail don’t. Some servers sometimes have the issue of reusing message identifiers and both clients would show the wrong content for the mail. You’d have to force a resync of the whole Mailbox to fix this.

Also: A backup of the mailbox would be unaffected by any server-side change.

most imap clients wouldn't even notice. Once that message is downloaded there's no reason to download it again.