Art nouveau may not be top of mind when you are in Florence, but it exists.  Here’s a quick article on the subject.  Also, bear in mind that the “Liberty style,” which is what art nouveau is known as in Italy, abounds in Lucca.

http://www.firenzeturismo.it/en/informazioni-utili-2/itinerariafirenze-2/itinerariatema-2/2417-art-nouveau-in-florence.html