Pretty much exactly what you’ve described.

Where I am ya don’t been a permit for a shed if it’s under a 18 square metres, so 6x3m sheds are common.

You could look in to off-grid / caravan appliances, thereby saving on a smaller inverter, but they tend to be around 3x the price of regular appliances.

Highly recommended going for 48v system if you’re starting from scratch to save on ridiculously large diameter cables and stupidly high amperage you’ll be dealing with with a 12v system.

I did a repair this week on a poorly designed 12v system that had a 12v to 230v 7amp (1600 watt) inverter powering a 230v 10amp cook top in a camper van. That cooktop was pulling 235 amp from the battery through a very hot 175amp slow blow fuse.

Which is great if you want to melt the fuse post and the supply cables and… I found the fault before the fire started.