Fear of this Battlestation
tldr; Park your Colossus in orbit over one of your planets to increase stability and reduce crime. Or your Star Eater in orbit around a star without a aetherophasic engine.
Whether you are using your Colossus as a deterrence or using it to crush all opposition beneath your heel. Sometimes you might not be in a state of total war. (I know, crazy right?) You paid good alloys for it, but now it is sitting in the garage like some vintage sports car you only bring out for Sunday driving.
Don’t you wish that you could put that Colossus to good use even during peace time?
Say no more. Now you too can implement the Tarkin Doctrine on your own systems.
“Fear will keep the local systems in line. Fear of this battlestation.”
Now when you place your Colossus in orbit over one of your own systems (specifically using the enter orbit command when you right click on a colony), you’ll quell criminal unrest and give a small boost to stability. They don’t know that you can’t blow up your own colonies. But they won’t call your bluff. Sure productivity might take a hit from all that “fear” but the boost to stability will more than counteract that.
Depending on what kind of weapon is on the Colossus, you’ll get a different effect. A Deluge Machine over an ocean world is actually kind of a boon, but over any other world and it’ll be almost as scary as a World Cracker itself. This modifier only lasts a few months, but will continue to affect the colony so long as the Colossus remains in orbit.

It should be noted that boosting Stability is a deceptively powerful effect, giving either 0.6 to 1% production for each point (depending if its above or below 50%). The intent of this mod is that this is less about boosting production (although the less destructive ones still do that) and more about reducing crime and preventing low stability events. Ideal use case are problematic planets with low stability or when that criminal syndicate opens up a branch office on your own planets.
You can also park your Star Eater in orbit around a star without a aetherophasic engine to apply a smaller stability effect to every planet in the system.