It was even more convenient to conduct the investigation in secret. So, the official investigation team could only be considered a decoy, while the secret investigation was the real official one.
They only discuss some of their team's preliminary plans because they do not yet have any official plans. As their team was sudden and had only begun, they needed to adapt themselves. Well, everyone was aware this was only Spade's consideration for Rave.
And one other reason was that it was already late, and Arren needed to take a rest. Possibly the most significant reason for him
As part of their initial plan, Levin would mostly communicate with Rave and exchange the information that they both gathered. Although they have talked and exchanged information before, this would only make it official.