iMessage on iPhone does not sync with Mac

Just what is wrong here. It should be a straightforward process of just flicking on Message on my Mac and all my iPhone iMessages should just be there - automagically. But noooo. It's not that simple - obviously. I read through the dated articles on this, and still nothing works.

What I do have when, entering Messages, are outdated texts from eons ago. So despite having checked and tweaked settings (as advised), nothing syncs.

What I want is a straightforward way to get my iPhone messages syncing with both my Mac Pro (10.15.4) and my iPhone (13.3.1) without requiring the need for a computer science degree to get it working.

Anyone got a solution?