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I don’t think that is your well pump switch. That looks like the HWH pump override relay box. When the HWH leveling calls for air, it provides power to the 120V pump AND bypasses the well pump switch.

It is unclear to me when you say one side has power and one does not exactly what you are saying because it could mean two different things. One side of the HOT relay has power, and the other side of the contact does not. OR the hot side has power, and the neutral side (white) does not. Which is exactly how it should be.

First thing I would check is the breaker on the inverter feed. It will be a small AC breaker box on the driver side in the inverter bay.

 Correct, the picture was not of the pump switch.   See attached new pic.  What I circled is what has power.  Checked breaker at inverter and all was well there.