There's a way
Turn on Time Machine and stop automatic backup for now.
Now go find the drive you used for Time Machine and check the name of the file it generated on your oldMac, probable the name you gave to the computer + an extension like Porsche27.backubundle or .sparsebundle.
Now the drive and the Time Machine drive.
Well, take the name before the dot and go to System Preferences > Sharing and name your Mac with the very same name Porsche27.
Wait a couple of minutes while your Mac connects itself with the old backup file as if it was one of its own.
Now you can open Time Machine application (that classic windows with a rule of dated on the right side) and see that macOS sees the old backup just as it used to and you can recover only what you need.
After that you can turn automatic backup on again or even delete this old file and make a new one based on this fresh install you're running now.