I just ran a number of experiments using different MIDI styles and each and every style correctly played and notated Cdim, Cdim7, and Cm7b5. I inputted the chords as Cdim, Cdim7, and Cm7b5. So it appears as the chords are correct on the MIDI side of BiaB.

I surmise that on the RT side what you get is what the performer played. I have played a dim7 chord in place of the sheet music's dim chord many times, as long as it doesn't interfere with the melody.

Note that I have never seen a dim5 anywhere, but that may be because I input all of my chords myself. YMMV
Sometimes, when you cry no one sees your tears
when you hurt no one sees your pain
when you're sad no one sees your sorrow
But fart just once

64 bit Win 10 Pro, the latest BiaB/RB, Roland Octa-Capture audio interface, a ton of software and some hardware