Apparently people can't enter my DLC giveaways

Check the screenshot (it says that he's missing the base game although he has it). As I have said in the original post: the person just won the game from me yesterday, he doesn't have the DLC yet and still can't enter the giveaways.

That means that as long as steam is learning about a game, we effectively cannot give away DLCs for them?

Looking at this and the endless amount of future games that steam will have to learn about, I hope that CG soon finds a workaround for this. Maybe disabling the check of possession of the base game for such DLCs and a big warning message over the enter button (or check mark that has to be set) could be a quick solution for them.

This. Steam API can't detect base game on account, so "missing base game" pops up here at SG, resulting in not being able to enter giveaways for its DLCs.

Ask to have what removed? The DLC from SG database or my giveaway? Also, it's not a 0 CV game.
To me it seems more likely that the reason behind the issue is what nhahtdh suggested.

It's not a Steamgift bug, it's how Valve stupidly set up their "learning about this game" system by not even reporting it to the API, giving lots of trouble to ANY site that checks for game ownership.

Or just make a giveaway of the base game and give the soundtrack as a bonus, it's usually just 1p.

I did that sometimes.

There's no need to do anything. It doesn't affect anything in any way, and your giveaway slot is automatically refunded.

On the one hand, one can consider that anyone who'd bother to add the game to account would have pounced on the free DLC key themselves. Add in that interest in DLCs tends to be niche to begin with, and it's possible that a repost of the giveaway would change the outcome [as, after all, many Tales of Candlekeep DLCs ended without any entries, back when, but were able to manage some later on].

However, gauging off the comments within the thread for the freebie promotion, it's most likely the base game is misconfigured. Given that there's no real benefi to posting freebies through the giveaway system [other than, I suppose, in artifically inflating one's sent-won ratio for the sake of those who only give profiles a casual glance], you can always simply give the key away directly or through a keydrop, if you're still wishing to give it away to SG's community.