Never really did this in three dimensions so unfortunately I don't have exact advice on how to properly code this, but here are some ideas about enemies, or how to approach this stuff:
I think the first bit might be to ask yourself what exactly you want from the combat.
One thing you can do is boot up a similar game and just try and pay attention to what exactly the enemies are doing. Stuff like when they attack, how they move around, how aggressive they are and so on.
Another thing that might help is to look at 2d twin-stick shooters and see what kind of enemies these tend to have, since there's a good degree of overlap between these kinds of games. Obviously it's not a perfect fit, but it might again be a good place to get some ideas.
The last thing that might help with finding a good starting off point is just build an enemy that chases down the player and doesn't do anything else. Once you've managed to get this thing working, you can start adding some variation. Maybe one enemy chases the player down, but stops at specific instance, another one could chase them, but retreat after they got attacked?
Also seeing that big ship in your gif makes me think about just focusing on capital ship combat instead? That way you can kind of concentrate more on creating specific projectile patterns that players have to avoid?