The Kthid don’t have a way to cheat the speed of light the way the HEF does… so they need very powerful drives to accelerate between stars in a reasonable timeframe. They do this by harnessing the power of black holes, creating what is called a Singularity drive, or a Kugelblitz drive.
For concentrated energy packed into a small area, it is incredibly difficult to do better than a black hole. Mass has energy… and the idea that black holes don’t give off any of that energy and it is gone forever is a bit of a misnomer because of a phenomenon called Hawking radiation. An interesting quirk of Hawking radiation, however, that makes it useful for starship propulsion is that the smaller (less massive) the singularity is, the quicker it gives off Hawking radiation… an incredible amount of energy. Despite being smaller than an atom, the black hole would weigh more than 700,000 tons and would give off hundreds of petawatts worth of energy over its roughly 5 year lifetime, billions of nuclear bombs worth every second. By using particle mirrors, Hawking radiation provides the impulse needed to push a starship up to an eye-watering 72% the speed of light.
The singularity cannot be refilled, but it can be recreated… usually by using solar power satellites gathering energy and focusing them into a single, inwardly focused pulse of light and radiation. The pulse of light needed is the equivalent of the sun’s output for 1/10th of a second, or .01% of its output gathered over 10000 seconds. For this reason, the first thing any Kthid fleet or ship will do when they arrive in a new system is create solar power satellites for use in refueling. Those satellites can also be used like pushing lasers to help slow down an incoming ship, bouncing photons off of the Aegis field.
For further reading, I suggest this – https://www.researchgate.net/publication/293633217_Acceleration_of_a_Schwarzschild_Kugelblitz_Starship