Storage is not an issue. It's been solved for decades. In fact, energy storage is amazing and cheap now, thanks to smartphones and EVs. You can buy consumer level batteries for very very cheap.
Battery tech is awesome, but I think you're overselling it a bit. We've barely started figuring out grid-scale battery storage on Earth. There's 2 big reasons the Moon is going to be much much harder:
1. Batteries are heavy, and space ain't cheap. Current launch pricing is about $1.5k/kg to LEO. The Moon will be more, it's further away. Even if Starship brings that down by a factor of 10, transportations costs are still going to be astronomical.
2. The day-night cycle on the Moon is slow. Your batteries are going to need to be able to store half a month worth of power. You'll need 15x more batteries on the Moon than you would on Earth.