Mens attire Southern Italy/Sorrento

It feels like in general Europeans don't get down with shorts the same way Americans do. Even in hotter weather it's not common, but it also wasn't rare down that way. You'll see people dress the gamut. I'd say dress as you feel comfortable, button down shirts are the classier choice. Bring a pair of shorts and pants. Also, resign yourself to the fact that you can't keep up with an Italian person who's trying to dress nice.

Coastal areas in the US are shorts, Tshirts, maybe button down short
sleeves with boat shoes, sandals or sneakers, but that feels very
casual American.

Gosh, that sounds just like the Sorrento we observed when we were there! :O)

Honestly, Relax2gether, the town - and the coast in general - was very casual as far as sightseeing. You'll see everything from shorts to jeans to chinos. Rule #1 (with some exceptions, where visiting churches is concerned) is not to dress much differently than you do at home as you'll be most comfortable that way: no need for a completely different wardrobe, and clean and tidy will do. Rule #2 is to wear shoes you can walk in all day, up stairs and down hills and across all sorts of uneven surfaces: comfort trumps style when it comes to your feet!

I see that you are staying in a luxury level, 5-star hotel so you might want to kick it up a notch if intending to dine there once or twice in the evenings? I don't see any need for a sport coat (they don't appear to require them, anyway) but one nice pair of trousers or Dockers and a couple of crisp shirts should certainly do. One pair of shoes for your dinner attire should be all you need in addition to your walking shoes.

It may be cool in the evenings, if the wind comes up, so I'd pack a light jacket for taking passeggiata about town after dinner.

We went in October, took nothing but jeans and an assortment of shirts/tops, and didn't feel out of place anywhere at all, although we admittedly didn't eat at the very posh places (but we ate well!).

In Sorrento and rest of Amalfi Coast there will be service industry locals and tourists, don't think many Italians will be holidaying with you so your typical dress sounds like you will fit right in with your normal wear.
It is very causal, not like you are going to Milan where everyone is dressing to impress, this area is more casual and laid back where people are going to Holiday not to work.

Locals who if not working in the service industry you probably won't encounter since it will be end of Sept may be switching into Fall attire, it doesn't matter that it is hot and humid it will no longer be summer so won't be wearing the same thing as in the summer.

I stayed at a nice hotel in Sorrento that served what seemed like primarily a British clientele and dinners were quite fancy, most of the guests did dress up. Not suit necessarily but definitely pair of slacks and a button down or collared golf shirt as minimum to fit in.

If you will not be dining at the hotel than that really doesn't matter as the town's non-hotel restaurants will be more casual.

I appreciate The input and shared experiences. Some good points are made. Very much looking forward to staying at this hotel, which is an anniversary gift, but the outfits didn't come with it. 😎

so, I am starting to get a picture of what's getting packed and what's staying home.

I've seen local men in shorts in Italy and in Paris in warm weather. I even saw one young man with cutoff jeans, a business shirt and jacket and an attache case in Bologna. But men older than teens and 20s are in shirts, not tees.