Greek Islands in middle of March?

You could have a good experience with careful choices ... look to stay in towns, on islands where there's a substantial permanent population, so that there will be activities and facilities. You'd have the bonus of interacting with locals going about their lilves, not flocks of tourists. If there are also colleges there or nearby, another contribution to activity

Some places I think of:
NAXOS - 10,000 Naxians year-round so port town pleasantly active -- bus schedule sparser, but useful for visits to beaches and hillside villages
CHANIA, CRETE -- Also a permanent population, especially in surrounding "nea chora" ... and home of top-ranked Technical University of Crete. Good basic bus network for exploring.
NAFPLIO, in ARGOLID mainland -- Not an island, but on a peninsula surrounded by sea, so can have island feel. Large permanent population in surrounding "new town" and also a favorite getaway for Athenians, so things going all year-round. The Univ of the Peloponnese has its School of Fine arts right IN Nafplio, also the Harvard School of Hellenic Studies .. so I've heard there is an active arts schedule off-season.
RHODES - I'd guess this island would be Very rewarding in off-season... Rhodes town would be populated but not swarmed by cruise crowds, enough permanent population for shops/restaurants serving locals.

Pre Covid I went regularly to Greece in March. It depends very much on the island.

Syros, which is the capital of the Cyclades is busy all the year round and most places were open.

Santorini was dead with only a couple of open places. (This was twelve years ago. I can’t imagine the same is true now.) Sifnos and Serifos were also pretty much closed up.

Having said that I think you’ll find somewhere to eat pretty much anywhere.

I ended up mainly going to Crete - an island obviously but not what I assume you’re thinking of - or the Peloponnese. Nafplio is good out of season.

Janet and I were writing at the same time. I very much agree with her opening paragraph and her suggestion of Chania is a good one.

Until Easter time, ferries will be on limited winter schedules.