I notice that there's an option on Steam for a Deluxe version. Is this available through GOG automatically, or is it only available via Steam?

Nothing in the store. Do you have any details?

Possible explanations are:
A user-created module has ported the first game's story into the third engine. The UGC was actually assisted by the Harebrained Schemers, and is available for free.
The first game was released with Dragonfall — the second game — as DLC, but this is not as complete as the Director's Cut.

If so, however good it is, it isn't going to be supported in the future; the second game (like the Returns and third, Hong Kong) are all maintained separately by Gog, and there is no ongoing support for the DLC in the first engine.

But without any more information (I don't have a Steam account) I can't help you.