If you go deep enough, yes, it's the same engine under the hood as every Bethesda game since Morrowind, and before that going clear back to Oddworld: Munch's Oddysee and (believe it or not), Civilization IV. And if you dig even deeper, it goes clear back to Prince of Persia 3d. It was called NetImmerse, then Gamebryo, and now the Creation Engine. But while that DNA is deep inside, each release sees them tweaking it, adding to it, and so on. It's never been rewritten from the ground up (which is where a lot of the problems come from), but they do keep changing it to make sure it can handle new features.
So, yes - you can use some of the tools from previous versions, although it might take some hoop-jumping (I tried to open a few Starfield files in the FO4 GECK - the most recent version of their editor, and it just crashes instantly.) The problem is the changes/tweaks that they made to the engine and the file system means that they're not fully compatible. And if you manage to get one of the editors working enough to open the files, it still will not do so correctly, as nobody knows for sure yet just what's changed.
To give an example, there were a number of early Fallout 4 mods that were made using a Skyrim tool (TESVSnip.) Fallout 4 was only a few years older than Skyrim (about half of the age difference as FO4/Starfield), and a much closer form of the engine.) They caused many, many problems (one common example in FO4 was that all power armor you owned when installing one of these would be reset to its default values, and all modifications removed) until people learned to quit installing mods with .esp/esm files until after the real tools were released.
Random fact: .esp = Elder Scrolls Plugin, .esm = Elder Scrolls Master
