Best time of year to visit Greece?

It depends a bit where in Greece you want to go, and what you want to do. The islands, most of them, are more seasonal, Athens is pretty much year round, the Peloponnese and mainland sights can be done year round, though slower during "Winter".

We used to talk about a "shoulder season" where May and September were low crowds and good weather, but crowds now exist for most of the year, still, I would avoid June, July, and August for the heat and crowds, maybe September and into October if you want some Island and beach activity.

If swimming is not your thing, then after Orthodox Easter in April and May are nice.

If you are sticking to the mainland or Crete, then you can push earlier in the Spring and late in the Fall.

We were in Greece this year from early May until mid June. We were in Crete and Naxos. In early May Crete was warm in the day and cool enough to require a light jacket or sweater in the evening. By the second week the evening sweater was no longer needed.

By mid June the day temperature reached 35 degrees .

There were lots of people around but not crowded at all. In mid June half the sun beds on Naxos St George beach were being used and on Plaka beach there were lots of empty beach chairs.
I certainly believe the stories about Greece being very popular and crowded but if you go in May to mid June or mid September to mid October those times continue to be quite pleasant and not overcrowded.
Santorini and Mykonos are going to be crowded whenever you go.