Electrical – negligable voltage at receptacle

I suspect you may have something called a multi-wire branch circuit, which uses one set of three wires (rather than two pairs of wires) to handle as much load as two separate circuits. Current electrical codes require that multi-wire branch circuits must be powered by a pair of breakers that are interlocked so that whenever either one is turned off or tripped the other will likewise be disconnected, but some installations lack that interlock. Yours may be one of them.

If a circuit is run as two wires from the panel to the load, then when the breaker trips everything in the circuit will be de-energized. Likewise if a multi-wire branch circuit is run as three wires and both breakers are tripped or switched off, everything will be de-energized. Unfortunately, if only one breaker trips, devices on the side of the circuit controlled by disconnected breaker may receive a generally-small amount of current through devices connected to the live breaker. While such currents would generally not be large enough to cause a fire unless they were sufficient to trip the breaker on the other side, they could still be lethal to someone touching the "disconnected" circuit. Worse, a variety of factors may cause the amount of available voltage and current on the "disconnected" circuit to change unexpectedly, so even if a voltage tester shows that a circuit is "dead" that doesn't mean it won't seemingly-spontaneously become lethally energized as soon as the tester is put away.

Multi-wire branch circuits are cheaper to install than individually-wired circuits, and are perfectly safe when the breakers controlling them are properly interlocked, but can be dangerous when such interlocks are not installed.

I noticed some ants on the wall near the GFI box so I took apart one of the units that had failed (i.e., it would not reset, even with nothing on the Load side of the GFI) and found a fried ant across two terminals on the circuit board. Same with the other GFI unit. So the fix is clear - eradicate the ants and replace the GFI. Interesting that an ant can do that to the GFI. Seems like the manufacturer should seal the electronics. Dust could probably do the same thing.