SolipsistSerpent's suggestion is certainly the easiest way to make sense of the matter.
TRE would activate until the Types send their escorts away
The weird thing, I think, comes about when the antagonists are able to munchkin the number of enemies Anna faces, but the humans can't. If the antags have enough data to understand how Target Rich Environment works, surely the UN has even more, and they will be looking for ways to make it trigger in every battle--not just using an impromptu swarm of garbage-tier drones.
The end result is a merry chase where all low-level antagonists are trying to run away from the engagement while Anna shouts "FACE ME!", the UN orders her to contain but not to actually kill them (general orders would, in fact, be to run
deeper into Antagonist territory, as they only have so many Type Zeroes while an unlimited number of mooks), and the strategic goal is to corral an increasing number of low-level antagonists (inflated by as many UN plants as possible) into the battleground.
There would be extensive tests concerning what actually counts as an enemy. Anna would end up fighting lions, bears, and nuclear-capable pterodactyls. If Caitlin wasn't already an Antagonist, she would certainly be planted into the battlefield with the falsified memories of being one.
The UN would start sending fake Annas in order to force the low-level mooks to run away from the battleground, only for a swarm of conventional Valkyries to descend upon the unguarded targets or Type Zeroes.
It would be delicious, delicious chaos and one-upping.