I just bought this DE version, and no
there's no 'classic' version in my library prior.
Are the DLCs apart of the DE or not????

"The Definitive Edition delivers the ultimate experience for Outward players.
It is not just a visual overhaul, but naturally combines the new mechanics and features from Outward and both DLCs, The Soroboreans and The Three Brothers, to make it feel like a brand new experience."

It's not clear, and at this very moment I'm getting a warning that I cannot purchase the Two DLC (for this game) that are in my cart. Why the cloak and dagger routine? Are the two dlc combined in this edition or no?

The Definitive Edition is an overhaul of the original game with the DLCs included and more smoothly integrated.

The DLC pages pretty much only exist as a way for people who owned the original, which can no longer be acquired on GOG, to upgrade to the DE cheaply.
As I've grumbled about in other posts, it's not my favorite approach, either.