Does Bambu use any open source software in their firmware?

They do use some opensource components in the X1C AP board, like vsftp, mosquitto, paho-mqtt-cpp, linux kernel. Email opensource@bambulab.com to request the source code.

But as far as I know, the main part of the firmware is written by bambulab. The firmware does not use klipper or marlin.

Kinda old thread, but learning atm, found this the other day in settings, so the preference for flavor having only 1 option makes me wonder

How or where did you get that? From the UART?