With your MacPro 3,1 setup, the upgrade will work perfectly using Dosdude1 Catalina patcher either by creating USB installer or the Install to Machine option. If you wish to keep Mojave than create separate APFS container for clean install and then optionally choose the Mojave container to move over applications.
Software Update can not be used for in-place update from Mojave to Catalina.
You should use a different connection, such as DVI, for the patcher install. Apparently not DisplayPort.
I expect that you can't use the DisplayPort output for the patcher install.
And, that's part of the patch, so when the install is complete, you can then switch back to the DisplayPort for your needs.
Nice, it got answered. I was in the discord today asking and the forum was quicker. Nice.
We have the same computer except I have the gtx 770 and much less RAM. Good luck upgrading to Catalina and apfs. I backed up my drive today in preparation.