I watched Tuesday night's show earlier this evening. They ran a full set of credits, over a new visual of the outside of the theater with the marquee lights gradually shutting off.
I noted Louis Cato is still listed as Music Producer. As Batiste is listed as musical director (and also has a producer credit), I'd guess Cato is involved in generating a lot of the music used in sketches and other prepared pieces. To my ear, he sounds like he's often singing some of the songs used in cold opens (when it's not Brian Stack). And FWIW, I think he's doing OK during his conversations with Stephen.
I couldn't tell from the credits if there's an official new showrunner taking over for Licht. But I have heard Stephen speak to a Marcus a couple of times.
David