We're in Rome now - arrived last Saturday and are staying for a week.
It is certainly much less crowded than I recall from previous visits. For example, on Monday morning there was no queue (literally, none), to get into the Vatican Museums. Of course, parts inside were still busy but mainly only the Chapel and a few other pinch points. On Tuesday, at the Borghese gallery, I tried to estimate visitors whilst we were waiting to be let in - I'd guess well under 100, even though it had been nearly sold out when we bought our tickets.
Of course, in the parts of the city where the Romans live & work, there are still plenty of people and buses are busy. But in the more touristic areas, it's noticeable how empty most restaurants and bars are.
The only closures we've come across are the catacombs.
Rome is a great destination at any time, but fewer other tourists is certainly a boon to us (though, equally, awful for those businesses relying on the tourist market; I imagine it's even worse in the north).
How this will be by Summer, I've no idea. Hopefully, for the sake of the livelihoods of many, this isn't more than a short-term position. But, selfishly, seeing Rome without the crowds has been wonderful and I'm glad we came.
Edit to add - went to the Coloseum today. Incredibly, no queue for "buy on the day" tickets. I also started seeing more people wearing face masks. Mostly, they seemed to be younger people.