Americans eat TONS of filled pastry. We call them "pot pies", notably the hand held version...which can be bought at the grocery store from a brand called "Hot Pockets".
These are crusts filled with veggies, meats, and cheeses. There is also the basic pot pie which is made like a pie, but has all the ingredients a stew or casserole might have, encased in a crust.
Norcalbaker is right about the buns though, thats pretty much a British thing, as I don't know many other countries who eat a lot of filled breads. Here in America, we usually use some sort of pie crust. The Asians usually have small filled buns and breads, but they are more bite-sized desserts than bread.
Americans also eat a lot of Kolaches, which are small sausages wrapped in a roll and baked. Probably the closest thing you are talking about, that we eat here.
There are people who eat filled buns here, and some bakeries do sell them here, but they aren't extremely popular by any means. Some Asian and European style restaurants will have them on the menu, but they are more of an appetizer or lunch item here in America.
As for dessert breads or sweet breads, probably the most popular thing here in America is the cinnamon roll. It's made with a variety of bread doughs, and is sold, made, and eaten all over the country. There are thousands of different recipes for cinnamon rolls, but the standard recipe is just a simple cinnamon filling with simple glaze.
I will have to correct Norcalbaker on something though............eclairs, donuts, cream horns, and even chocolate filled croissant can be found pre-made in most grocery stores here in America. They can be found in the freezer section or in the bakery section of the grocery store. Having worked in many grocery store bakeries, I can tell you that we used to make all of that on-site in the grocery store bakery, but since the late 1990's, grocery stores have either invested in their own production factories or outsource the making of these products, as they are shipped to the stores now, ready made and frozen. All the bakery clerks do nowadays is remove them from the box, fill them, glaze them, put them into containers and place them out in the store for consumers to buy.
And actually, some of those eclairs aren't too bad. Cream horns are my favorite though.
As for the millennials, I haven't noticed any changes in the snack market. Twinkies, Ding Dongs, Ho Ho's, fried fruit pies, Oreos, and Chips Ahoy are still making billions a year selling these things.
I also haven't seen many instances where millennials want or demand "fresh" anything. If they want "fresh" they usually go through a drive thru at some fast food place, or a local donut shop that has a drive thru.
There are artisan bakeries all around, but they have always been around, as long as I can remember, so I really haven't seen any changes in that either. And most of these artisan bakeries are too expensive for the middle class of working people. A lot of these mom and pop bakeries and artisan bakeries have either had to lower prices to stay in business, move to a higher wage neighborhood to keep their prices, or just go out of business.
From what I've seen over the years, more and more people are getting lazier and lazier to the point they can't even be bothered to learn how to operate a microwave, much less know how to boil water or make something from scratch. They want ready made, fast, convenient, and CHEAP. This is why grocery stores have gotten so big, physically I mean. Pretty much every grocery store wants to be a "one stop shop" for everybody.
So it's a lot easier to find all these snack items, even if they are produced in a factory and shipped to the stores frozen, before being placed out for the public to buy.
If this were 30 years ago, I could tell you what was popular here, what sold the most here. But now, since stores want to carry everything for everybody, and you can pretty much get anything you want............it's hard to say what the most popular breads, rolls, or pastries are. There are just so many to choose from, they pretty much are all the most popular.