approximate cost difference between seasons

Not sure there is a shoulder season anymore
Tourism is up everywhere almost all year now

Most costs are static- food, sights, trains

Airfare and hotels may be different

A lot depends on where you are planning to stay. If you are going to cities and the normal business travel is active during those months then hotel prices would be high season. If you are going to a rural area after families are back in school it might be the beginning of their low season. A lot depends on where you are going and what’s going on in those places.

I would not count on any reduction in prices nor crowds except, perhaps, November - February, excluding Christmas weeks.

As mentioned above, only hotel prices and airfare may vary. Everything else will stay unchanged year round. Mid September to Mid October will be very high season in art cities (e.g. Florence, Venice, Rome) so hotel prices will be high. Seaside resorts will be in shoulder (or even low season), so prices will be lower compared to the summer months (basically when schools are closed. The only exception is the Amalfi coast and the Cinque Terre, where it will still be quite busy, maybe not as busy as July-August, but not low season for sure. Tuscan countryside will be still busy as well.

As far as airfare is concerned, that is a total unknown to me. Airfares can be all over the place between April and October. However generally it’s always cheaper to fly November through March.

Rental cars are through the roof from June through August (especially July through August), when also many Italians rent. Outside of that, it’s a bit better.

Agree. Mid September to Mid October is still a busy travel season in Italy. We are here now (early November) and have found many hotels will offer lower rates when we walk in. The downside is the shorter days and potential rain.

I think it depends on where you are planning to stay. I agree with the other comments but Puglia for example mid September can still be quite busy and more expensive, while mid October a lot lot quieter.

there are so many pricing sources on the internet these days, it should be simple to play around with dates and see what happens.

As noted, the seasons have all kind of mushed together these days. You go on the dates you can go, and pay what you have to pay.

I wonder if the main difference might be some added flexibility to book later at a reasonable cost. We went last October and were able to book hotels in Lucca and Cinque Terre at the last minute at a good price. I somehow think we would not have had the ability in September. I suspect it won't make much difference if you plan to book everything ahead of time.