The reason there's no toilet seats on toilets in Italy is because most Italian people don't like to sit on public toilet seats.
And also because people in Italy have stood on toilet seats and have actually broken them.
There are no toilet seats in public restrooms throughout Italy and apparently you still haven't encountered Turkish-style toilets (bagno alla turca).
Hygiene conscious Italians prefer not to sit on a public toilet seat.
Apparently, the toilet seats in Italy are there originally but, then, they break.
The seats break because people stand on them.
People stand on them because they are not kept clean enough to sit on.
Either the proprietors decide there's no point in continuing the cycle, so they consign their toilet to the ranks of the seatless.
Bidets are found in pretty much every Italian home and hotel but are seen as a little too fancy for public restrooms.
(Though even that is not unheard of).
They are almost always standalone bidets, which are located next to or close to the toilet.
Squat toilets are generally non-existent in Northern and Western Europe.
France and Italy are an exception and have some squat toilets remaining in old buildings and public toilets because they used to be the norm there in the early 20th century.