Though the heat levels of this pepper can very greatly, it meets your other two requirements. It's Italian and you can save seeds as it is an heirloom. Ausilio Thin Skinned Italian pepper.

I have had peppers from this variety that seem to have no noticeable heat and others that are much, much spicier. I really like it.

https://www.seedsavers.org/ausilio-thin-skin-italian-organic-pepper

From the same source listed above, you might also be interested in Beaver Dam. Very large, conical peppers with walls as thick as bell peppers. It has a short DTM, and moderate heat. You can lessen & customize the heat by removing all of the seeds & placenta, but may find the heat level after cooking to your liking. Beaver Dam is my favorite pepper for canned salsa.

Pepperonchini, hot wax peppers, Italian Long Hots AKA Italian Roasters are all good too. Some of the Corno de Toros can have a wee bit of spice to them, and some Cubanelles get a bit of heat and work great in Italian cooking.

Some of the Spanish like Guindilla for thin walls, and Padrons or hot paprika peppers for thick wall works- so to Black Hungarian peppers for a very mild to sweet jalapeño type, a fave of mine. Rocotillos are nice too. A Turkish fave of mine is Urfa Biber- those are great fresh, dried, smoked or not with just a bit of heat..

There's lots of lower scoville peppers that work, try using the term "seasoning peppers" in your search.

Uh oh, my garden junkie curiosity has just been triggered. I might have to try all of these! Not sure about my zone though, zone 5b/6a. Sometimes our summers are perfect for peppers, other times not so much.

I have grown Hungarian hot wax peppers for pickling and salsa, but they are little too . . . I duuno "acrid" for soups and sauces in my experience.

There are several charts & lists of hot peppers (ranked by Scoville heat scale) that are a good way to find peppers at your preferred heat level. This is one of them:

Peppers ranked by Scoville heat units