iMessage stuck saying Syncing Paused on iPhone since iOS 17.0.2

Ever since I updated my iPhone 15 to iOS 17.0.2 about a year ago my messages have never been able to sync to iCloud, the Messages app has an annoying banner along the bottom that says "Syncing with iCloud Paused" and if I go to Settings > iCloud > Messages and press "Sync Now", it says "Syncing with iCloud" for perhaps a second or two and then goes straight back to "Syncing paused".

I've tried everything I can think of from signing out/in to iCloud, resetting all network settings, even backing up to iTunes (Apple Devices) and restoring it from a backup. I raised an Apple Support case 6+ months ago and went through largely the same troubleshooting steps, got bounced around a bit, until eventually being told the engineering team are working on it and it'll be fixed in a future update.

We're now all the way on iOS 18.1.1 and I've kept my iPhone up to date with every version in-between, yet this is still happening so I'm not holding out much hope.

Has anyone figured out a clever way to resolve this issue themselves?