The shed as an of site backup is a good idea.
We live in the shed (it is really its own entire stone building) during our full house renovation, so I have already run electrical and cat6a to the shed and have an old router in AP mode there.
Hooking up one of those NAS boards or a 2nd hand old PC there would be a good backup option.
Sodium ion batteries are going to be the solution. 18650 packs are already out and perform economically. Since the molecules are so much bigger, energy density is only like 60% of lithium based solutions, but they have a very wide temperature range and are incredibly more inert and safe and density isn't a problem for bulk energy storage.
The hurdle to overcome in inverters dealing with the very wide voltage span and bespoke charging ICs, but definitely possible and within 5 years will probably become a lithium iron phosphate competitor.