No, Sanguinaria is from the church side.
Basically the agent side got to 'be Benika's friend' spot first so the church can't pull the same, instead they're just going to armstrong their spy into the mix via the threat of exposing Hibai (right after she got past a spy test too)
It is not confrimt yet. Though your idea make it sound werid. so, she just exposed herself to another spy who who totally not in her own side. So you want to spy this girl, who is sus. but you tru to spy her and spot a spy who spying her, that not your spy. That sound like you should more aware of the spy than the target. and you basically have the upper hand, knowing something they don;t. But, you go and expose yourself ? let spy together on that girl? so know you let them know you exist instead of spy on all of them ?
if am kinda think they are like free-lance, which is just like how MC get the job til now, that maybe both work with the agent. so they dont know each other. The thing i feel missing is the job is not like a hunt price, like in John wick or so, but given by the agent and they select who to do the job. So it must be really a bad manament job to make such a thing to happen.