Even pre-pandemic the Scrovegni Chapel tickets had to be purchased at least one day ahead of time. I don't think it typically sold out early; I got my 2015 ticket just one day ahead, at the tourist office. But I was staying in Padua for several nights, so that was an easy solution for me.
Someone who visited Venice shortly after Italy opened up reported there's now an entry fee for San Marco itself; previously the church was free and you only paid to see special areas, like the Pala d'Oro--which I guess many visitors did not do. Imposition of an entry fee reportedly has caused really significant ticket lines, aggravated by visitors' need to decide which combo ticket they want to buy when they reach the ticket counter. I think you have a choice between going very early in an effort to minimize the amount of time spent in line and accepting there's going to be time wasted and planning San Marco for mid-day when they (reportedly) have the lights turned on.
Another issue reported by the aforementioned poster was a significant line at the Doge's Palace. Rick's advice to buy the combo Correr/Doge's Palace ticket at the Correr Museum seems not to work now. It sounds as if the Secret Itineraries Tour (which sells out early) is a good line-beating strategy.
The usual pre-pandemic guidance for the Vatican Museums was to pay for an early-access tour (cheapest option being on the Vatican website itself; commercial tours are more expensive) to get in ahead of the general entry time. I have no idea whether visitor levels are low enough now that entering the museums during regular hours is OK.
