Hey there!
Good question!
I know you’ve changed iPhones. However if you are using the same Apple ID on all devices and have iCloud Messages enabled on all, they should be syncing, (Given enough time as mentioned).
Can you check both your phone and Mac?
iPhone:
Settings > Apple ID > iCloud > Messages.
Mac:
Messages (On the top) > Preferences > iMessage.
Just to make sure iCloud is turned on for both?
For the Mac you’ll see a check box to “Enable Messages in iCloud” on the phone, you should can switch iCloud Messages on or off.
Otherwise if you don’t use Messages with iCloud, or use more than one Apple ID, then you may have to try something else, as suggested.
If you don’t, also make sure Text Message Forwarding is on for your Mac in Settings > Messages, and of course that you’re signed in on both with the same Apple ID and have the same settings configured.
Hope something here helps!