Unable to view Messages on my MacBook

Initial message - Since moving to a new MacBook Pro (M1 2020), messages are not syncing between my Macbook and my iPhone. Some messages appear on both devices but a number of contacts can't be messaged from my Macbook, and messages from them on my iPhone don't appear on my Mac.

I have checked that the Apple ID is the same on both devices.

I have updated to macOS Monterey but that didn't resolve the issue.

UPDATE - I followed the suggested actions of ensuring the software on both the phone and the MacBook were up to date, restarted both devices multiple times, and followed the actions in the article "Use Messages in iCloud".

The issue persists. It appears that text messages from other iPhones are viewable on the MacBook and iPad, but messages from Android / Windows phones are not. Those messages are only viewable on the iPhone.

I am using Messages in iCloud.