GFCI Trip while AC charging if Jackery 5000 plus is connected to manual transfer switch?

My new Jackery 5000 Plus seems to be working as expected, aside from one questionable behavior.

If the 5000 is connected to a manual transfer switch and also charging from its AC input, as soon as I turn the AC output on, the GFCI trips on the receptacle that the 5000's AC input is plugged into (the GFCI receptacle is not on the transfer switch). Additionally, it seems like even if the 5000's AC input is coming from a completely separately derived system (eg not connected to the house at all), turning on the 5000's AC output while connected to a transfer switch trips the GFCI on the receptacle from the seprarately derived system.

Here's some relevant info on my setup and test scenarios.

  1. Manual transfer switch was installed by electrician 20 years ago with 50amp generator input. This switch does NOT switch the neutral. The neutral and ground wires are bonded at the main panel. The Jackery had no problem running all of the circuits on the transfer switch during a multi-hour test run.
  2. The GFCI trip happens with the 5000's AC input connected through an energized circuit from the main panel (not on the transfer switch). The 5000's AC output has to be on for the GFCI to trip. Just having the transfer switch connected doesn't cause a trip. Also, the transfer switch main breaker was in the utility position, not the generator position (didn't try generator position).
  3. Charging through the 5000's AC input works as expected if a non-gfci receptacle is used (again from the main panel), even with the 5000's AC output turned on.
  4. I also attempted to charge the 5000 using 120v AC (15amp) from two different EVs. In this test, one EV tripped and the 5000's AC charging stopped as soon as I turned on the 5000's AC output. A second EV (Hyundai E-GMP platform) did not trip and charging through the 5000's AC input continued with the 5000's AC output active.

My guess is that the 5000 is bridging the neutral from the AC input to its AC output and thus to the transfer switch. Since neutral and ground are bonded at the main panel (through the transfer switch), I'm guessing the return current for the AC input is flowing to ground through the main panel. But that's just a guess.

If this is the case, does anyone know if this a safety issue or is a problem for any other reason? I'm particularly interested in the case where I'm charging the Jackery using its AC input from an E-GMP platform EV (Hyundai, Kia). This appears to work fine, but I'm guessing the return current is still getting bridged to the main panel neutral or ground and that seems bad.

Any insights on this would be greatly appreciated. Thx.