The timing on the SWIO interface needs to be within a few hundred nanoseconds if you want decent bandwidth, but I suppose there's nothing stopping you from running it on a slower and less real-time GPIO pin. You'd just need to swap out the implementation of the PicoSWIO class, the rest would be identical.
It's a programmable, parallel data bus, like you'd get on an old school micro to access external rom and ram. It'll DMA to/from the Pi's RAM, and has programmable timings for read and write signaling, so it's not at all like bit-banging GPIOs. The only question is if it's usable for your debugger project, as it's not meant for that.