Germany does mandate M&S tire use only in snow and ice conditions. Basically, you're on the hook when you drive around on summer tires in these conditions, although there is no general mandate to have winter tires.
Italy, however, definitely has regional M&S tire mandates - especially in Milano and Bolzano provinces. In the Aoste Valley, there's a blanket winter tire rule in effect from Oct.15 to Apr. 15.

BTW, German law stipulates a minimum thread depth of 1.6mm (the TWI bars are set at that level). Should your tires have been really bald, that car wasn't roadworthy no matter the road conditions and should not have been rented to you.

My own experience with Sixt is pretty much the same as yours - don't expect them to be forthcoming with anything. I had to settle for whatever vehicle was available on the lot with winter tires or a diesel engine regardless of what I had reserved all too often with them, and that's one big reason why I rent with the competition nowadays.
Pursue the chargeback, that'd be likely the only avenue with any meaningful outcome. Pretty simple, actually: you had a confirmed reservation for a vehicle with AWD (the Ghiblis here in Switzerland have AWD) suitable for a winter time excursion to Italian ski resorts, and that service wasn't delivered.