Most people recommend the simplest setup with MP3s for minimum risk, but a number of people use BiaB successfully for live gigs. FWIW, I've used iRealPro for live gigs, though BiaB sounds much better.

I'd suggest a proper external sound module like a Focusrite, Presonus, whatever. The headphone output can be a bit temperamental in my experience. The connectors isn't hugely robust and hum can sometimes be a problem. Proper sound modules sound far better.

Jazz relative beginner, starting at a much older age than was helpful.
Kawai MP6, Korg M50, Ui24R, Saffire Pro 40.
AVL:MXE Linux; Windows 11; Win8.1: Scarletts
BIAB2022 UltraPAK, Reaper, a bunch of stuff.