In Florence Dec 24-28, what will be open?

On Dec 24 most grocery stores you should plan to be inside a grocery shop by 7:30 pm or 8pm at the latest. That's the closing time for most. Some larger chain stores are open a bit later (9pm) but they may not be near your flat. If you tell me where you are, I might be more precise.

On Dec 25 most stores will be closed. If you don't have food by then, you might be stuck with restaurants (the ones that stay open on Xmas day). Booking in advance helps. If everything fails the Catholic organization Caritas has soup kitchens open for the poor on Xmas day.

Dec 26th is a holiday and the 27th is a Sunday. On both days many grocery shops, except for the largest chain stores, like Coop or Esselunga, will be closed. Restaurants will be open, so you won't starve.
Monday 28th all stores are open.

Tell me your flat address and I'll give you more precise info. Florence is my town.

As Roberto has pointed, everything is open on 24th and everything is closed on 25th. I would not bet on much being open on 26th and also the 27th looks pretty grim.
If everything fails I would try the upper floor of Mercato centrale; it is not cheap - consider it as more an alternative form of restaurant than a market - but it could be open all days. Also the ethnic shops run by Indians and Pakistani are likely to be open all the time.

Mercato Centrale advertises itself as being open 365 days a year so that one looks like a possibility.
Posted hours are 10:00 - midnight

Now, I do not know if opening hours/days apply to ALL shops and restaurants within the mercato but it would make sense that some will be open on the 25th,26th, 27th if the center itself is not closed.

https://www.mercatocentrale.it/en/contacts/

https://www.mercatocentrale.it/en/shopping-at-the-mercato/

https://www.mercatocentrale.it/en/mercato-centrale-firenze/

The ground floor of Mercato Centrale is an ordinary food market - well, in the last years some stalls have become more tourist oriented - and it is open till 2pm on working days only.

The upper floor is more modern and has ready to consume food - you buy the food and you can eat it on the spot seated at a bench; a waiter will come to bring you something to drink if you want. It also has some restaurants. They say they will be open 365 days a year - but it looks more like a place to eat something than a place to shop food to bring home for cooking.

Yes, good catch, lachera. The hours are for restaurants are upstairs; the market below does have different hours (Mon. - Fri. 7.00-2.00, Saturday 7.00-5:00 (but different during summer) Market is closed on Sundays.

Thanks for the replies. We are staying very close to the Duomo, but are coming from the airport, so we will be getting into the city center closer to 7pm.

Thinking about it, Eataly in via Martelli is more likely than ordinary supermarkets to be open on festive days. They are basically a top range supermarket and 30% more expensive than other ones, but you can stock there.