Italian Beach/Mediterranean Honeymoon

If all you care for is a beach, then Sardinia is your friend. Sardinia has by far the best beaches in Italy and probably the entire Med.
Over the years I’ve posted several comments on Sardinia. I’ve linked some below, but you can use the search function up above to find more.
Not many in this forum have visited the island as it is a bit off the beaten path for North Americans (although it’s very popular with Europeans). It’s a big island and it will easily keep you busy for two weeks. A car is a must for a proper visit.
https://community.ricksteves.com/travel-forum/italy/sardinia-a4b6bf34-12f0-4f41-aa46-cc7c08ab1f7f

Sicily also has some nice beach spots, especially in the Aeolian islands, but Sicily has so much to offer in historical sights that it would be a waste just to go to a beach.

The Cilento area in Puglia also has great beaches (mostly cliffs mixed with small sandy coves).

The Amalfi Coast is great too, however that is purely cliffs. The few small beaches are pebble coves.

There are of course many more choices (Italy has 5000 miles of coastline), but the above are some of the most popular spots. September shouldn’t be too crowded no matter where you decide to go. Europeans tend to go back home at the end of August in preparation for the school year start.

Capri is luxury with prices to match. It may suit your requirements if budget is flexible. I haven't been there as it didn't hold any interest to me, I'm not interested in fawning over celebrities and ostentatious displays of wealth. Sorrento could be a perfect match without the eye watering prices of Capri. I can't give any advice about partying in Sorrento as we've always been there with young children. If you were to visit Sorrento I would certainly take the opportunity to visit Pompeii or Herculaneum. I know you're not interested in museums/history but it would be criminal not to visit one of the world's most fascinating historical places which is a 40 minute train ride away.

Sardinia has a reputation for quiet, exclusive breaks and a fantastic food reputation. I've yet to go but I'm waiting to be relieved of the burden of children and indulge in my love of food without having to deal with a checklist of likes and dislikes.

If you're going for 10 days (realistically 8 days) then I'd stay in one location, I'd even stay in one location if it was 12 (really 10) days. A break as you've described pretty much fits the description of a typical beach holiday for us Europeans and for the duration of 7 or 14 days staying in one location is pretty much the norm

I think Sardinia is probably the best answer, but I'll plug my favorite spot for beaches: southern Tuscany--anywhere from Castiglione della Pescaia to Capalbio. There are a couple of fancy resorts but also plenty in the way of apartment rental.
I'm a sea/beach lover and my other favorites are the Lerici area in Ligurua and the Cilento coast in Campania (the southern bit of it reminded me a little of Croatia actually--scenery-wise, but there are also sandy beaches.)

Greece is another option. Many Greek islands have pebbly/rocky beaches but I have found gorgeous sandy beaches on Naxos, Paros and Lesvos. Probably other islands as well. If you’re interested in exploring this idea, post your question in the Greece forum.