I recruited and outfitted a team's worth of secarios before receiving this mission. The mission doesn't recognize that I've already got a working team in place, so I can't complete it.

Do I have to recruit a second team to complete this mission?

Yeah the mission is to buy 3 sicarios, you will eventually need 3 teams anyways so it wont matter in the long run.

Sure, but if I've already bought them have I not already completed the mission? The system not recognizing that is keeping me from moving on to other missions.

If I recall correctly, if you have 3 or more Sicarios then it's enough to just recruit a single Sicario

Explained trigger