MAC pro late 2013 updation

You must install High Sierra 10.13 at some point to move to any MacOS beyond 10.13 High Sierra.

Are you using the original Apple boot SSD?

at what stage does it fail, and what is the error message, exactly?

You may have some software added that interferes with the upgrade.

Try running the upgrade while operating in Safe Mode, where no third-paty add-ons are available.

Try stepping up MacOS versions starting with Yosemite