How can I get my Macbook Pro to sync Messages from my iPhone 7 Plus, it has suddenly stopped

First try simple things like deactivating the service on iCloud in Messages preferences. Then try signing off of Apple ID/iCloud in macOS System Preferences.

Also deactivate and sign off on the iPhone (choose to keep data on the phone so you sign back in and everything will be the same).

Also try rebooting in Safe Mode (start your Mac while holding Shift) and then reboot normally and check if it helps.

Nice!

Glad it worked for ya!