There are a few programs out there that go a little way to what BiaB does, though none are remotely in the same class or remotely as powerful.

JJazzLab is quite good. MIDI only, I believe. Cordsheets only IIRC.
Impro-Visor ditto, but a slightly different intent. It will create improvised solos, one can enter notes in notation.
MMA (Musical MIDI acompaniment). It has no GUI itself and is entirely script driven, though there are a couple of OK-ish GUI front-ends by third parties.

Those do all have the advantage of being free or donation-ware. They do all run on Linux.

I hope PGM won't mind me putting them here ... my version of their own "dare to compare" page.

Jazz relative beginner, starting at a much older age than was helpful.
AVL:MXE Linux; Windows 11
BIAB2025 Audiophile, a bunch of other software.
Kawai MP6, Ui24R, Focusrite Saffire Pro40 and Scarletts
.