To me, drama means any kind of disagreement or problem, no matter how little. This came, originally, for finding problems in something. For example, if we want to agree on which costumes to use for the play, we can have a civil discussion and then agree on something - or you can throw a fit and say that the costumes are shit, and that your idea is better and that nobody is listening to your idea and that, because of us, the play is gonna be much worse now and blah blah blah they're being dramatic. Explaining the way I use the word dramatic is probably best done with a few examples because of how little the general definition of it actually means.

If you get pulled over by the police you would hope to be let on your way with as little drama as possible. In this context, that would mean no extra questions beyond what is normally expected. You hope that you don't have to step outside the car to do an alcohol or general driveworthiness test. You hope that you don't get flagged for the condition of your car, that you don't get a citation. Of course, being pulled over by the police is drama in and of itself, but a police check can be pretty routine, or it can be dramatic.

In general, any kind of adversary or “enemy” in any context is drama. When you play Helldivers 2, I use “drama” to refer to the amount of enemy presence. More drama means more enemies means less control over the situation and higher risk of injury. You see, the term “drama” can be used as a noun or an adjective, because I also like to use the word “dramatic” to describe the attitude of an enemy. Bile Titans in Helldivers 2 are typically a relatively tame and predictable enemy that don't tend to cause problems or throw fits of any kind, but every once in a while they will do things that are more “dramatic” than usual, so I will call them out as being dramatic.

Drama can also mean complication. For example, in a strategy board game you might be able to get rid of one of your pieces, but doing so might involve a lot of different steps, moving a lot of existing pieces around, possibly losing the string and risking messing up the board irreversibly. This potential move is then very complicated, involved, in short “dramatic” or “prone to cause drama”.
In the same vein, if you're kind of stuck, or if your situation is difficult and it's hard to move forward/get out of that situation, your situation can be described as dramatic.

So if it's a problem that (1) is more problematic than I think it needs to be or (2) I don't want to have, it's drama, and the entities related to it can be dramatic.