ARPAT is the Tuscany Region environmental agency that monitors all kind of environmental pollution including air.
I don't know if they have month by month data, but you can click on any dates below since 2018 to see what PM2,5 was on that day.
https://www.arpat.toscana.it/temi-ambientali/aria/qualita-aria/mappa_qa/index/pm2.5/tutte/16-10-2023
I think generally (just based on the Italian news I see daily), the bad months are especially in winter (Dec-Feb) when I guess the pollution from traffic and house heating combined to high atmospheric pressure (typical of winter) on dry days, make the situation worse. July/August is probably bad too, on those high pressure days. I think your best chances are in early spring, where the occasional rains clear out the air.
Also it varies with location. The worst area of Tuscany is the valleys west of Florence all the way to the coast, and the Arno Valley between Florence and Arezzo. If you stay in the mountains/hills outside of those spots, the air quality seems to be below the warning level all the time.