The first one is Nautilus. The File Manager. The 2nd one what You get for saving or picking Files isn't Nautilus. That is the File Picker. They look similar but these are 2 different Programs.
Chance of that are very slim, I'm afraid. Upcoming versions of the Gnome shell (which powers the whole desktop experience in Zorin OS Core) will have a much better integration between these two components. For now, though, we can only wait and live with what we have.
Upcoming as in a-few-months or as in a-few-years-or-possibly-never?
It seems at least the bookmarks are the same and present in the file picker, so I just have to use them instead of favourites.
They're pretty likely to update the GNOME version with Zorin 18, but I wouldn't expect it sooner. There is no hard date on Zorin 18, but the question has been asked and opinions given quite a few times. I don't usually tell people "search the forum," but in this case, as often as it's been asked and answered, and given the lack of an authoritative answer, that's really the only way to get a broad impression.
As far as I know, no. That is ... baked in the Desktop. With Gnome 47, Gnome changed that. From this Version Nautilus is file Manager and File Picker. So, with that, You should have that I guess.
Depending which Gnome Version will come in Zorin 18, maybe You could have that there. But for this, we have to wait until it will be presented.