This can all be a lot simpler if you use an inverter with a UPS function. In that way you only need two shore power outlets, one to the inverter and one for your battery charger.
All other loads (under 10 amps) can run from the inverter, including the A/C (with appropriately powerful...
Some Growwatts have a stupidly low voltage limit on the solar input others have a high minimum. Google the model and check the pv voltages. It might just be a matter of re-arranging the panels to get the right voltages and amps.
SPH 6000 specs below (is this yours?)
I see there is a start...
So 50% discharge from lead is around 12.2 volts. You said the low voltage cutoff (of the fridge) is 9.5.
If you discharge lead acid to this level you will probably get around 10 cycles from it before it dies!
Just run it straight off the battery.
Yes it is a bit of a crap shot as to the quality you get but that being said many people here get a good result from AliExpress.
Follow the threads here, you will get a feel of what's good and where not to even try your luck.
I've just ordered 4 200 AH LitoKala cells from the LitoKalaVariCore...