icloud full can i upload messages to Mac?

No.

Messages are either in iCloud, or in backups, and there’s no easy way to restore messages from a backup short of restoring the iPhone.

For USD$0.99 per month, this problem goes away, at least for a while.

iCloud storage plans and pricing - Apple Support

Again, no.

Acquire more iCloud, or delete some of the conversations.

This is the mirror of the how-can-I-restore deleted conversations, and there’s no good option there, either.

Backups can save messages, but restoring those requires restoring the entire device.

Log some feedback for the folks at Apple: Product Feedback - Apple

Just to be clear, iCloud is not a back up service. It is for sharing between computers, people and devices. And, as you can see in your illustration we can select specifically what we want to be shared via iCloud. For back up and restoration, you will need to set up a back up process. If you haven't already done so, get an external drive to use for back ups and you can use Time Machine or other apps to schedule back ups. Otherwise, it's only a matter of time until you will loose your data.