Is the PY4G HVAC unit compatible with Nest Thermostat?
Yes the PY4G unit is compatible with the Nest 3rd Gen Thermostat. I'm guessing that the quote from the manual about power-stealing is to ensure users use the common wire and don't rely on smart thermostats' power-stealing.

My issue was that I had 18/8 coming from the outdoor unit that met with 18/5, but only 4 wires {Y-G-W-R} were connected. The junction was hidden behind the aluminum flashing that protects the main duct before it enters the crawlspace. This is why I didn't see it when I was in my crawl.

I connected the blue wires, got a good reading on the multimeter, the Nest Thermostat no longer gives an error, and my HVAC is working again. Shoutout to @ThreePhaseEel for the help!