I am not sure about the station itself but in the nearby hostel „SafeStay“ (5mins walk) it should be possible to leave your luggage for a small amount of money (but maybe call them if you can also leave it as a non guest)

Since many yrs there is NO locker/usual type of storage in any IT stazione. Result of putting bombs in one long time ago.

On my week long IT trip last week I noted that in most major stazione-esp. those with many turistici there is now a private company offering it-all manual, and I think from what I saw (not used myself) also with a kind of airport screening. Prices were quite high-per hr and not per day (as is usual in lockers). But I have not been in Pisa.

It was for many yrs indeed the usual advice to check for such places on station forecourt-or even that modern helpyourself: google. The information would usually also know and point-after all a very common question.