Yes, baseband, modem f/w and the operating system work together but don't have to talk to one another.
A great read about be REX, from Qualcomm that goes into more detials - https://fahrplan.events.ccc.de/congress/2011/Fahrplan/attach...
All the fun Qualcomm PDF's seem to be missing from the net now, but there were more official/confidental PDF's that went into details besides this: https://en.wikipedia.org/wiki/REX_OS
BUt even reading from the old dead CDMA2000/eVDO standard you can see more of this too - https://ftp.unpad.ac.id/orari/library/library-ref-eng/ref-en...
And more on "what is a qualcomm chipset" https://ftp.unpad.ac.id/orari/library/library-ref-eng/ref-en...
Yes, these links are not for GSM, but Qualcomm makes GSM and these carry over as a standard, and these 10-15yr old slides are amazing and should be archived too - they used to be public even on Qualcomm sites too.
But thank you for the https://yatebts.com/ link - that is so cool, what I do with diagnostic and fun tinkering is with Qualcomm Tools that I no longer have access too. QPST, QXDM, etc.