If My Heart Had Wings - Deluxe Edition - Game and Soundtrack Bundle bug in giveaway

Something is misconfigured on Steam's end, there's likely nothing staff can do.

Typically you resolve the problem this way:
Contact SG support [it's going to be slow these days, so be patient]; Let them know you want to post it as the base game, and that you want to then do a Change Giveaway Game once the giveaway completes. Post the giveaway as the base game.

Once the giveaway completes, follow-up on that ticket and let them know they can now update the game. Make sure your winner has commented on your giveaway with what version of the game they received, and to link that comment in your ticket.

Staff has helped me with buggy packages in the past in such a manner. :)