Maybe if it was possible search by steamlink for game or steam id?

It's possible to search by game appid, example:

https://www.steamgifts.com/app/2215430

https://www.steamgifts.com/game/MRYxs/in-the-dark

Why not search for the game in Steam DB or Steam store? Then you can search for the game's app ID in the giveaway archive.

Maybe I just misunderstood the assignment... but it feels counterintuitive to add "omit" search parameters. With the Steam API system and store id that link these identifiers to a game exclusively, why would you use omit parameters, that you already need to know, before making the search? Do you plan to search for these items multiple times daily, that it's worth essentially "bookmark" them? And then any new release would mess it up.

If you're looking for a green rectangle in a heap of shapes, you should pick a green rectangle. Not omit circles, triangles, hexagons and every not-green colour one by one. In my opinion a function for "only this, and no more" would be a lot more useful.