Time Machine Restoration - Catalina

I religiously backed up my Mac Air to a portable Drive which was running Majova no problems.

Bought myself a brand new Mac Pro with Catalina but unable to restore the files from my Time Machine Back up disk, which I had made sure was up to date with latest backup. The Mac Pro is loaded with Catalina but will not even recognise the disk - a My Passport.

Apple Support were unable to access my Mac remotely for some reason so visited the Apple Support Desk at local store with no success.

Any thoughts, help please?