LOL
Batteries have chargers. Unless you disconnect the charger you are running your charger you are running off the charger power supply which is usually not of high quality since the battery doesn’t require a quality power supply.
The power source is solar and the powerwall doesn't get power from the 'grid'.
Maybe it is a real improvement but often people in your situation are experiencing confirmation bias.
You don't know me, nor do I know you, so you should think before you judge someone else's experiences.
People in your situation. That's Archie Bunker right there.