Better for you to determine if the structure in the bay is failing first. Sometimes the bay is suspended on the outside of the home and the structure fails for one reason or another. If that is the issue, then fixing that will eliminate the slope.

https://diy.stackexchange.com/questions/173071/advice-on-supporting-a-sagging-bay-window

It does not need to be level, only flat and most often within an 1/8" over 10'. You say you have a bay and then show the bottom of a door, can you post a picture of the entire room? Probably if only the bay area is low, you would use a self leveling compound.

The bay window area was always low. I don't think it's sinking/failing. There are no cracks or areas of sagging. I think the builder just didn't build it level.

It starts at the edge of the foundation and goes out to the windows/door so about 2 feet. Ignore the split vinyl. That's just a seam split not where it drops off. It starts dropping at the edge of the door frame. What kind of self leveling compound do you recommend?

We measured the entire kitchen floor with a laser level. See measurements differences in picture. There are slight bumps and dips but we have 2 main concerns. First, across its entire width the floor slopes down 1/2"-5/8" over about 8 feet starting from a relatively flat dining area. Toward the nook windows the slope is 3/8 to 1/2" over much shorter distances with the worst in the vicinity of the door.

Presented with the measurements a floor store representative said the difference can't be more than 3/16" over 10' (mfg specs) and told we'd need to get a contractor to level the floor before they can install.

We don't know what kind of contractor to find or how to find them. We are considering using floor leveling compound and doing it ourselves. Anyone have any advice?