In the context of mobile, "baseband" colloquially refers to everything "below" the application processor (I guess technically stopping at the RF mixer). The physical layer protocol is carried out in the digital domain by the "baseband processor", which is also running code that takes care of the higher level session protocols.

So yes, this generally includes all bits of protocol below the simplistic IP and AT-command based session interface that's exported.

(My idea for "SIM proxying": The link between a SIM and the baseband processor is a simple serial link. So as long as latency requirements could be met, this serial link could be tunneled over IP, allowing one to rent a SIM card that wasn't actually in their possession).