The Growatt does indeed have a setting to limit charging current (specifically for using a generator). Or at least every manual for them I've read did.12 awg is for 20A, 2400W at 120V or 4800W at 240V. Possibly you would want a 10 awg 30A cord.
I haven't used that inverter, but see if there is a setting for how much current it should draw from the input. It may be able to let you connect a smaller generator, draw no more than your setting, produce additional power from battery when needed.
Do you have a generator yet? Dual fuel would let you use propane (never goes bad like gas), tri-fuel would also use natural gas, cheap and convenient if available at your house. Some are electric start and some inverters can automatically start and stop generator.
Since she indicates she has 200 AH at 24v capacity lead acid, 0.2C is probably appropriate charge rate (correct me if I'm wrong).
That would be 40 amps. From the manual:
Program 02
Maximum charging current: To configure total charging current for solar and utility chargers. (Max. charging current = utility charging current + solar charging current)
24V model: default 60A, 10A~140A settable
Program 11
Maximum utility charging current Note: If setting value in Program 02 is smaller than that in Program 11, the inverter will apply charging current from Program 02 for utility charger
24V model: default 30A, 0A~60A Settable
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