I am bouncing around between a few of my favorite space sim games right now and there is something I noticed just now: While you can enter asteroid fields or planetary rings and fly around dodging giant space rocks, all those rocks just sit in place and maybe rotate around. None of them move.
You can’t affect their trajectory. They can’t collide with each other, and you will never have to adapt to an asteroid coming out of nowhere coming toward you.
In fact the only game I can remember having moving, dynamic asteroids is literally "Asteroids."
I would love to play a game where you can have a space battle that feels like the scene in Star Wars Episode 2 when Jango is trying to take out Obi Wan. Having to dodge weapons, asteroids, and account for the asteroids movement and changing trajectory based on collisions/exploding.
Shit would be badass.
I suppose you could say KSP counts. You can grab asteroids in that one and move them around.
Another, more relevant one is Star Trek: Legacy. I believe this mission fits your requirements. The game is abandonware, however, so you’ll have to find some means to acquire the game.
Maybe Star Trek: Armada? I remember a few missions where you have to evade some space hazards like asteroids. You can pick it up on GOG.
Maybe Starcom: Nexus? It’s a 2D space game that incorporates drift when you fly around. I don’t remember if asteroids matter all that much, but you can ram other ships to break their components.