As expected BiaB works fine on the new OS. One thing I noticed is the background for title and style shows an odd purple hatched effect. If you select either it goes back to normal but the effect shows through around the edges. This makes no difference to the operation of BiaB though as far as I can tell.

There is one thing that now looks odd, as Apple have redesigned all of the app icons for a more uniform look. The BiaB icon now looks rather big, but makes no difference to the running of the app.

Logic Pro X and Garageband have also had updates including new content.
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MacBook Pro 2020 - Big Sur 11.4
BiaB UltraPak+ 2021 Mac, (503)
Yamaha SLG200N
Epiphone Les Paul Studio

Logic Pro X,
Xtra Styles 1 - 10. Loops-with-Style PAK 1 & 2. Multistyles PAK 1.