In your shoes I'd just monitor the websites of the places I wanted to visit. As you say, today's situation may not be tomorrow's. I wouldn't want to buy (likely non-refundable) entrance tickets way ahead of time, so I wouldn't care what the current policies are except for places that might sell out crazy early, if any. (I don't have current travel experience in either Germany or Austria, so I don't know whether any of the places you mention call for ticket purchase well in advance.) I'd start checking websites perhaps two weeks before the departure date unless other posters highlight places where it would be risky to wait that long.
Pre-COVID there really weren't all that many sights so popular that tickets could sell out before the day of the visit. Except for Barcelona (which had about six of them), those were mostly special, limited-access options at major sights (the floor of the Colosseum, the royal apartments at the Alcazar in Seville, etc.) or small venues. It's possible, of course, that health-related capacity controls may add additional sights to that list. If you're interested in taking tours, that's a different situation.
I did some preliminary checking of northern-Italian museum websites during the summer. The websites of a lot of the more prominent museums were encouraging advance purchase of tickets. In some cases that was mandatory, though sometimes only on weekends. In other cases things were sort of weasel-worded, with advance purchase being encouraged but evidently not required.
