I’m an idiot, and was testing continuity to ground while the BY starter wire was connected to the solenoid, so of course it showed continuity. Removed it from the solenoid spade, no continuity. Anyways, that was just an aside rabbit hole…
Received the new ignition switch yesterday. Boom, turned over just like it should.
Bottom line, the aftermarket ignition switches from cheap unknown brands (sold through zcardepot), might not be great quality. This new one I got from Amazon is “standard motor products” brand and will hopefully last longer.
Nonetheless, I learned some new things on how the ignition switch is wired to the starter. Special thanks to @SteveJ for all the pointers.