This sounds like a FOSS utopian future :)
There’s a few projects that have started towards this path with single-click deployable apps, you could even say HomeAssistant OS does this to some extent my managing the services for you.
I believe one of the biggest hurdle for a “self hosting appliance” is resilience to hardware failure. Noone wants to loose decades of family photos or legal documents due to a SSD going bad , or the cat spilling water on their “hosting box”. So automated reliable off-site backups and recovery procedures for both data and configs is key.
Databox from BBC / Nottingham University is also a very interesting concept worth looking in to:
A platform for managing secure access to data and enabling authorised third parties to provide the owner authenticated control and accountability.
Instead of one super chunky battery, how about a laptop with replaceable batteries, in combination with a UPS?
UPS is so you can actually replace the laptop battery with a spare one , even during a power outage. Just run the laptop on AC from the UPS while changing batteries. Or see if you can find a UPS with a long lasting battery. Entry level ones only have like 15-30 minutes of battery life though, since they’re more intended for safe shutdowns or brownouts.