Hi ThirdeyePhoto,
It sounds like syncing Messages to iCloud and are inquiring about the time it takes to do so. We’re happy to provide some information.
The amount of time it takes will depend on the amount of data being uploaded and your network speed.
When uploading data to iCloud, it’s recommended to have your iPhone connected to a Wi-Fi Network and a power source. If you disconnect, your upload will resume at a later time.
We also suggest making sure that you have enough iCloud storage space available: Check your iCloud storage online or on any device - Apple Support
Thanks for using Apple Support Communities.
Take care.