One thing I’ve read to “force” an iMessage sync with iCloud is to just backup your device. I’m not sure if that applies to only backing up to iCloud, or to a computer as well. But it doesn’t hurt to try!
If you still have your older iPhone with all the iMessage data on it, I think you can turn off iMessage in iCloud on that device and let it download everything to that phone. That will take time. Then do a full iPhone backup to your computer or iCloud, then transfer to the new phone as you normally would.
Of course with anything relating to downloading from iCloud, many things matter. I’d imagine things like your device being on charge, connected to Wi-Fi, and “downtime” periods where you’re not likely to be using your phone for a long period of time will affect how quickly this process takes. I wish there was an option to just download/sync everything immediately in one go
If you still have your older iPhone with all the iMessage data on it, I think you can turn off iMessage in iCloud on that device and let it download everything to that phone. That will take time. Then do a full iPhone backup to your computer or iCloud, then transfer to the new phone as you normally would.
Of course with anything relating to downloading from iCloud, many things matter. I’d imagine things like your device being on charge, connected to Wi-Fi, and “downtime” periods where you’re not likely to be using your phone for a long period of time will affect how quickly this process takes. I wish there was an option to just download/sync everything immediately in one go