Your home’s power input is also 240 volts in the US

It's not actually 230V in Europe, it's 400V. Between each pair of the three phases, that is, between phase and neutral there's 230V. (If there's a neutral and you don't create it locally, different topic).

...but I'd actually have different doubts about using the whole thing in the US: Your plugs. Schukos aren't meant for the purpose and only code for up to 800W when used to backfeed. That's almost 1/5th of their 1 hour continuous rating. With those flimsy tinfoil plugs you have you're going to need special outlets, or hard-wire them.