iPhone messages sync with Mac but not from Mac to iPhone

My iPhone just broke and I replaced it with a new one

My messages/imessages are set up to transfer and sync from the cloud between my iPhone and my Mac

I formatted my new iPhone via iTunes of a backup from old iPhone

However, there are some messages I see on my Mac in iMessage that I want, that occurred after I had done my last backup (the one that my current phone is based on).

When I plug my iPhone into my Mac I see in iMessages that new messages are updating and coming in to my Mac from my phone, however, it's not occurring the other way, where the old messages from my Mac are syncing to my iPhone, does anyone know why or how to fix? thank you!