So what you're encountering is most likely getting into the launcher and then the game hanging on a black screen. It would appear that the problem with launching the game is a missing folder in /home/.local/share/Paradox Interactive (to my understanding that's like the equivalent of the Documents folder from Windows). This folder gets created on the first launch of the game, but for some reason it doesn't work like that out of the box on Steam Deck (or Linux), so let's fix that.

1. Go into properties of EU4>compatibility>force the use of a specific compatibility tool and set it to Steam Linux Runtime. This should actually get your game running, but more importantly, Europa Universalis 4 folder in /home/.local/share/Paradox Interactive gets created. You can close the game when it gets to main menu; we're done with this compatibility tool, the performance of it is less than ideal.
2. In properties, turn off the compatibility setting we just used, so just untick the "force the use of a specific compatibility tool" (this will make the Steam Deck return to its default compatibility tool).
3. Now launch the game again, and in the launcher tick the fullscreen option since fullscreen seems to give the best performance (though it should be on by default).
4. Set every video setting to low or off.
5. Go into Steam Input through Steam button>controls>configure and work out your key binds because the default ones are pretty abyssmal.

Voila! You should be ready to play! The kind soul from reddit, that helped me figure this out, said that there are at least 2 other versions of Linux Runtime that are not as outdated and might provide a better performance. You could also try to force fullscreen on Linux Runtime through command console to see if that helps too if you feel so inclined to use those tools.

Kind soul from reddit: grotaclas2
A reddit threat where it all began: Do you know how to run EU4 on a Steam Deck?

Don't forget to rate the guide, so that more people looking for this solution can find it easier!