Mmmmmmm. Powerwall.That is 130 Ah at 120V, so technically correct, but misleading.
Better is to say it needs 14 KWh.
A tesla powerwall 2 is 13 KWh, so close enough.
That is about $7,000.
But you also need quite a bit of extra equipment, plus installation.
So you are looking closer to $12,000.
A standard good LiFePO4 battery, like I added to my camper, is 100Ah at 12V, at about $700.
You would need 12 of those to run that heater for 2 days.
Plus a simple inverter/charger.
So around $9,000.
1) Solar hot water heater.
Solar heating panels + large hot water tank.
You store energy as very hot water in an insulated tank, not electricity in batteries.
Harder to control, but WAY cheaper.
2) Gas heater
Small on demand heater.
Note that #1 and #2 would need battery backup also, but only for controls and pumps, not heat.