Today I went under and had someone push the pedal in, I can confidently rule out the master cylinder. It's either from the slave cylinder or where it enters the transmission.
It could be the clutch fork in the internals, it sounds just like
this (no rattle like he shows later on). I'll see if I can pull back the boot and spray grease inside.
Edit: I took the boot off, wiped down some of the moving parts and sprayed a bunch of lithium grease on (as shown in video I linked). The noise has completely gone away, success!