I think you are saying that when the breaker is on, the pump runs. The new pressure gauge reads 20 PSI. So if the pressure switch is looking at 20 PSI also, you would expect the pressure switch to stay on.
Get a pressure gauge with a garden hose thread. Put it on the drain tap that is often at the base of the pressure tank, a laundry tap, or the water heater drain, or a hose bib. If there is a big difference in the two pressure gauge readings, something is clogged probably.
See if you can run a wire or pipe cleaner or something through the paths.
So now it wont fill the tank all the way. It puts about 5 gallons but the pressure gauge only shows 20 psi and the tank feels empty but I can drain about 5-7 gallons out of it but the pump wont kick off.
You get about 6 gallons of water under pressure from your system after turning off the pump switch/breaker. So it seems logical that that water was in the pressure tank and is being delivered from there.
Try knocking on the bottom part of the pressure tank. You might be able to tell difference vs when you knock vs higher up.