I was just in Florence a couple weeks ago. I stayed in the Oltrarno which is still dominated by local Italians, even if tourists inevitably find their way there. That's also where you'll find many little studios of craftspeople and artists -- especially on the streets San Niccolo, San Frediano, and Santo Spirito. Wander and look.
Look on "The Florentine" website (for expats) for upcoming events. That's how I learned about the annual Taste food trade show. For 20 Euros, I spent hours tasting cheeses, olive oils, sweets, etc. and chatting with vendors. Alas, that's only once a year.
There was recently an article in The Guardian about the Sant'Ambrogio neighborhood. I missed the market, but wandered the neighborhood which felt very Italian. I also visited Le Murate, a former jail that has a cultural center with free events (of variable quality).
There are some lovely tiny free churches with amazing works of arts and few tourists. I particularly enjoyed the Cenacolo di Sant'Apollonia while listening to a podcast from "Rebuilding the Renaissance" dedicated to its Last Supper fresco.
Something newish (since 2019) is the Museo Villoresi perfume museum. I'd never heard of this perfumer, but he's legendary among people who know the Italian artisanal perfume scene. The guided, interactive visit was a nice change from the visual arts and food.