What's the wheel diameter? Those look like they might be from the +1 era. Remember +1?
I think you mentioned it has old tires on it. Take a look at comparison tests of the BFGoodrich G-Force Comp 2 A/S Plus when you're ready to replace them. Got some for my car about a year and a half ago on my indie mechanic's recommendation (they're basically Michelin construction) and they're great. A beefy looking tire from all angles, too. I put the stock size on my car (it had some Yoko Advan tire on it) and the BFG has a much larger contact patch.
https://www.discounttire.com/buy-tires/bfgoodrich-g-force-comp-2-a-s-plus
EDIT: Looks like Plus 1 and 2 is still a thing. I was thinking of when it was a new thing back in the days when your Scirocco was born... and before.
The shorter sidewall and older, harder tires are probably contributing to the stiffer/harsher ride you mentioned.