Same here. They started early mid game, since every AI empire seemingly had the prio to hack them.

Since then, I used console 'damage 1000000000' (in words: 1 Billion) to stop them wasting my entire game - 400 mio might be enough, but it needs to be applied in 1 go or else they'll all heal in a day or 2. And yes, my admirals are all >lvl10 with repeatables way over 50 times stacked.

(In prior versions of the game, one possible strategy was to use loads of minor ships, since the stellarborne ships one-shot nearly everything. However, this does not seem to work anymore,
as way more damage is replenished than can be dealt this way - at least, that is my impression
atm.)

They are easy to beat. I play iron man mode only and by the time that they spawn, you can have about 10 fleets with 4-5 mio. fleet power each as a meat shield. By defeating the Phanon Corps, you can get 2 herculeans. With the fleet Meat shiled, you can win vs them (and i have capped repatables at 20x with the extra defines and changes mod) ACOT Sigma tech is enough. You have to have your tech maxed out. You should have about 120k tech points income and like 50k alloys income per month by the year 2330+. Its totally possible with iron man.

I'm using Quasarcraft (from another mod) to destroy them.
Stellar Systemcraft (from Gigastructural Engineering) is too slow and idk why it's destroyed instantly when fighting Gatekeeper