Instead of erasing the Mac, you might want to get a spare external SSD, format it as an APFS drive, and then install High Sierra onto it. (Hopefully you would be allowed to do this.). Or clone your Monterey installation onto it – then detach the external drive, erase the Mac, and install High Sierra internally.
After that, you could start up either from the internal SSD or the external one. High Sierra may allow you to run 32-bit applications, but its version of Safari is very old. Even Firefox 115 ESR stopped getting new features some time back, and may not be getting "critical security updates" from Mozilla for too much longer. So you may not want to run High Sierra all of the time - only when you need to for backwards compatibility reasons.
You can upgrade a Mac Pro (Late 2013) to Monterey,, so you may want to upgrade the Catalina installation at some point.
How to download and install macOS - Apple Support