AC500 and Floating Neutral Question

My apologies if this question has been asked, although I’m trying to not make assumptions that someone else’s situation is identical. I’ve got a inverter generator with a floating neutral and my understanding is the AC500 has a floating neutral. I have a bonding plug for my gas generator, but it’s not necessary when plugging the gas generator into the generator subpanel (I’m assuming this is grounded). For sake of completeness, the generator subpanel uses 30A 120V, so the AC500 by itself will work just fine.
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What I’d like to do is use the AC500 in standard UPS mode plugged into the subpanel. I would expect that I wouldn’t need a bonding plug to do this, for the same reason I don’t need it when the generator is connected.

However, I’d also like to either use it in UPS mode, then charging it via a gas generator, in the case of an extended power outage, or plugging it into the main power while the subpanel is set to be powered from the generator. The last part would be in the case of us leaving on vacation and wanting to make sure that things like the sump pump had power in the case of a storm where power was knocked out.

In the case of either of the above, would I need a grounding plug either in the gas generator or the AC500? Not sure why this is so confusing.