I've had this type of behavior on many coupled approaches with a large number of aircraft in FS2020 (still getting 2024 set up). In all cases the "aggressive pitch-down" occurred when I released the AP.
For instance, if I maintain coupling all the way to the MAP, the aircraft (could be any of them) will immediately go out-of-trim with a pitch-down (even though it should maintain the trim that was there). I've resolved this for the most part by simply uncoupling at least 100' above the MAP - this usually results in a stable glide path and the trim being spot-on. I've always attributed this to a fault in the MSFS AP though maybe it's an issue with my stick (Thrustmaster T.16000M).
I've never had this happen with the Starship, though that may be due to my early AP release procedure.