Not using RB
I use Logic and BIAB Mac (2021)

Some observations

1. A direct drag of a RT from biab mixer to Logic does not do anything although the drag appears to be toting an AIFF file. The dragged file icon simply disappears when dropped in the Logic Tracks area

2. A Single RT render drag/drop from BIAB via the top left corner export (.wav) works fine.
The output track has a long name that includes _single Render SGU_name RT# , Style description.
Much closer to what I would like but this means an interation through each track. Tedious

3. The whole song single file per track export creates a bunch of wav files that do not include the RT#.
These wav files are easily dragged into Logic en masse.'

Perhaps PG could add some configuration parameters (instrument/rt#, etc) to the file name construction in this safe file dialog box.

I might also get what I'm after using the DAW plugin. I tried the plugin early on with less than a maximized user experience. Perhaps its time to try it again.

biab2024(Mac) Latest Build
Mac OS Sequoia 15.0.1
Apple M2 pro 32GB Ram
Logic Pro 11