My contacts in Messages are not syncing on my new Mac

I just got a new Mac and my contacts are not syncing in messages. I have turned off/on contacts sync on both the new Mac and my iPhone multiple times, but the issue persists.

Please note, not all my contacts are missing on my Mac, but most of them are. Certain contacts like my immediate family members are shown in Messages….not sure why. When I search in the Contacts app in my Mac, I do not seeing the missing ones. I can add them one-by-one, but obviously this is not a good solution.

How can I fix this?