Messages on MacBookPro doesn't stay synced with iMessage on iPhone

Never used to be a problem until about a year or so ago (when I was still on Ventura), and seems to have gotten a lot worse on Sonoma. (Side note: I will not be upgrading to Sequoia any time soon, due to incompatibilities with software I must use, so please don't suggest that.)

All messages show up on the phone, but more and more frequently some don't show up on my laptop (which is where I prefer to send messages whenever possible). Makes it next to impossible to follow conversations on the laptop.

iCloud is active (and I pay for 50GB, with plenty of free space).

The Sync Now button does nothing.

macOS Sonoma 14.7

iOS 18.1.1

Hopefully there's a setting I'm missing, or maybe some sort of "reset" (cache, etc.) that will restore this functionality.