NOTE: in recent macs, the process is much much easier, as one can simply erase the contents and leave the base system alone. I don't think this can be done with the 2013 Mac Pro, though, so the following are the traditional instructions (it can take a while).
1) I suppose you know how to use Time Machine.
2) Make sure the backup is up to date.
3) Download Monterey from here:
How to download macOS - Apple Support
4) Make a bootable installer on a USB thumb drive
Create a bootable installer for macOS - Apple Support
5) Start your mac using that installer drive created in step 4.
Choose Disk Utility, select the WHOLE drive, and choose Erase, selecting APFS as the format with GUID Partition Map
6) Quit Disk Utility, and proceed with the installation
7) When asked, elect to migrate "from another mac, drive or Time Machine backup".
8) select your backup drive, and MOST IMPORTANT: check ONLY the user accounts you want to migrate, and NOT applications, settings or other files.
(If you check everything, you just get back to where you started!)