Can someone explain me what happened on this public giveaway and ended with only 4 entries?

The base game was bundled 1 day before your GA startet, I am not sure where (bundle; 95% discount). Assuming that not too many people own it and even less have synced their Steamgifts, there would have been very few users able to enter your DLC GA. As it was public, no harm done with less than 5 entries.
If it is a gift and the winner did not accept it, try to contact them again. If you do not succeed in doing so, ask support for a re-roll (might take some time).

It happens. If you level up the same giveaway, it not always follows a linear decrease in entries. But since it is a public one, you get CV for it even at one entry.
As for the winner, up until level 6 or so, scripting and bot using is strong and real. Their script may have entered something they don't want or own already, or maybe cannot activate for the lack of base game (it is not always properly recognised). Just reroll.

As Oppenh4imer already mentioned, the game was bundled the day before. The bundle also included the soundtrack. (I'm guessing that's were you got it as well)

Between people not syncing and the fact that most owners of the game probably had the soundtrack already, that's not a lot of users left to join in on the giveaway.