Venice, Florence, Pisa, and Rome in January 2023. Are reservations necessary?

If there is a period when lines are short, January through February is certainly one. I don’t think you need reservations at museums. Probably not even at the Uffizi or the Vatican Museums.
Reservations at restaurants depend on the restaurants, but except for weekends, they aren’t necessary even for the busiest ones in winter. If you go to a restaurant late, you find seats even on a busy day.

I have been to Venice pre-pandemic in mid January. There were no queues anywhere. We didn’t buy any tickets in advance.

The issue with restaurants wasn’t which needed reservations (none), rather which were open.

I've heard the Vatican has been particularly problematic. If you're going to be heartbroken if you can't go, I'd consider booking a guided tour or even just escorted entry on Viator that can be canceled until 24 hours before in case your plans change.

How many days do you plan to be in each city? With visitor levels in Italy running 50+% higher in 2022 than in 2019, I'm not sure experience from previous years is terribly predictive. I don't like to pre-book sightseeing tickets, either, so I'd probably monitor the ticket websites for the places I judged risky (including the Vatican and Borghese in Rome and the Uffizi and Academia in Florence) to be sure attractive time blocks on days leading up to my travel dates are not beginning to sell out. I think you always have to get the Borghese ticket in advance.

There are also some special-access things that I'd be worried about:

Rome: Scavi tour at the Vatican, tour of the lower level at the Colosseum, the Domus Aurea.

Venice: Secret Itineraries tour at the Doge's Palace.

I imagine there are some other special opportunities with very limited capacity that may sell out even in mid-winter.

Post-pandemic some museums required reservations. Those restrictions, once in place, often take forever (if ever) to remove. The Vatican Museums comes to mind immediately. Most others, if required, can usually be booked a day in advance, some even same day. The Borghese Gallery in Rome has required reservations for many years now. Tours may sell out. The Secret Itineraries tour mentioned above is very good and it's usually necessary to book some time in advance (and shouldn't be weather-dependent). I've been to Rome in February and small group tours filled up weeks in advance, because in off-season there are many fewer. And there were always lines for the Colosseum/Forum. In Florence you may have to wait in line for tickets to the Uffizi. In February there are lots of students who visit - maybe not in January though.

If you need a reservation for dinner, you can usually book it the same day.

Acraven:
Starting 1/18/23 we'll be 4 nights in Venice, 1 night in Padua, 6 nights in Florence (with a day trip to Pisa), 1 night in Orvieto, and 4 nights in Rome. We've spent some time in Florence and Rome before, so want to see the things we didn't have time for then and revisit the things we loved- hopefully with fewer people around (David at the Accademia).
I know we have to book ahead for the Vatican and Borghese, so we'll definitely reserve those. And we'll head to a soccer match in Venice, so those days will be set. I just want to be able to take advantage of nice days to walk around and save museums visits for rainy, windy, or snowy days. If lines aren't awful in January, we might be able to have our cake and eat it too. Just trying to get a feel for how possible this will be.

If you are visiting Rome on a week-end and you are interested in archaeology, the Domus Aurea tours must be booked in advance. You can book only on the official site, third-parties' guides can't work inside an ongoing excavation.

OP, your user name made me laugh out loud! Happy travels!!

Kayla P - Hopefully we'll have time to stroll through some characteristic workaday neighborhoods.

I think you've got enough time to do some playing-it-by-ear, but if any of the places mentioned in this thread are of interest, I wouldn't count on being able to just walk up and buy a ticket quickly.