No messages syncing on your iMac? I have observed that only messages that come from an iPhone will sync on my iMac. Non-iPhone messages are received via cellular on an iPhone, and desktop Macs don't have cellular.
On a Mac since 1984. Currently: 24" M1 iMac, M2 Pro Mac mini with 27" BenQ monitor, M2 Macbook Air, MacOS 14.x; iPhones, iPods (yes, still) and iPads.
