Software vs hardware-defined GNSS receivers
What exactly is a software-defined-radio in context of GPS? All receivers include CPUs for navigation message decoding, orbit determination, position fix and so on. The question is, how much of the processing is done in special purpose DSP-hardware and how much in the CPU.

It is quite common to have hardware for baseband processing (several millions of realtime complex multiplications/accumulations per second) but do the control loop filtering (several thousand realtime trigonometric operations per second) in the interrupt routine. Designs with weak microcontrollers (high interrupt latency, no hardware multipliers) may have coprocessor support for the filtering. Bit-boundary-detection, deframing, decoding, etc are low-rate threads without realtime constraints, so thats where software takes over.

Without any insight in a real world smartphone GPS design, I would expect that cellular baseband hardware is reused for GNSS reception. Realtime software processing may just eat up too much battery.