Determine if the inverter allows neutral to be grounded.
Use DMM to check voltages L-N, L-G, N-G
If it makes 120Vrms L-N and each of those are 60Vrms to ground, it is either floating or symmetric, split-phase 60/120V.
Connect a light bulb between N and G. if light bulb illuminates dimly, you can't bond neutral. If voltage N-G drops to zero, it can be bonded.
But check battery(+) to G and (-) to G, both AC and DC. If it now has 60Vrms on the battery, you may not want to bond it.
If battery voltages are acceptable, don't have AC riding on top, then bond N to G at the inverter, ground G, use a GFCI.
If the inverter isn't compatible with bonding of neutral, at least ground inverter chassis and ground wire to sump pump. The AC voltages present are only 60 Vrms which is less hazardous than 120 Vrms, but still a problem if you're standing in water. I'm not going to recommend use of such an inverter for wet applications (nerves and more still frazzled from my recent encounter, fortunately bone dry), but it is your life. Don't expose anyone else to such a setup.
I have suggested isolation transformers to derive a neutral that can be bonded, but many transformers are nasty loads for inverters. It can be done; I would try to use two 240V windings as 120V primary and 120V secondary. I've measured that and it works better.
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