my apple id will not allow me to update software on my mac pro

Purchases, INCLUDING MacOS itself, are tagged with your Apple-ID when purchased.

You can only upgrade the installed version when you supply the same Apple-ID as the original purchase.

so the two alternatives are:

• use the old Apple-ID -OR-

• make backups (which you should have been doing all along)

ERASE your Mac NB>> (this deletes ALL your files),

install the factory-original MacOS which is tied only to the Mac serial number, then

use your preferred Apple-ID to obtain upgrades to that version, then

restore your files from backup.

How did you initially setup the new Mac?

Did you Migrate from your old Mac during the initial setup?

Did you setup the new Mac with a different User ID than your old Mac?

Are you logged into your new Mac's Admin. User Account or into an Other User Account?

To update your Mac's software, have look at > Update macOS on Mac - Apple Support