Most professional data-centers will claim some sort of eco lable or running on 100% renewable, at least in Europe, but that means little if they still use a lot of electricity and thus displace other consumers to fossil fuel power.
The most sustainable is to host on a low powered device from home. We have a community with a special focus on that here: https://slrpnk.net/c/selfhosting
I'm hosting al my services on an old Android mobile with termux. Power consumption is ridiculous, not 100% sustainable but it is very low power. You could add solar panels and you're done.
In terms of performance, mainly for family use, I've never had an issue once I plugged it to an ethernet port.
No Docker unfortunately, it would require either to recompile the mobile Kernel or use QEMU and I believe it would have a big impact on the performances.
Basically this time the approach was: what can I do with an old mobile without rooting or anything.
Hardware:
Samsung S20
USB3 to Ethernet & charger port
128GB SD card
Sofrware:
Termux (android app)
SSH (OpenSSH in Termux)
Rclone (in Termux)
Sonarr, Radarr, Lidarr, Prowlarr (in proot-distro)
Transmission (in proot-distro)
Kavitha (in proot-distro)
Podgrab (in proot-distro)
Ombi (in proot-distro)
ntfy (in proot-distro)
Filebrowser (in proot-distro)
Vaultwarden (in proot-distro)
Homer with lighttpd (in proot-distro)
Since I wasn't able to install .NET Runtime in Termux directly, I used the proot-distro (Ubuntu) and inside I've installed all the services.
Services are started manually every time I restart the proot-distro (unfortunately I'm getting an error when installing Termux:Boot), it's a simple script so I'm not dying over it.
To keep the proot-distro alive I launch is with the screen command so I'm ensuring persistence even when the terminal is closed.
It's not a clean solution like docker etc. but I'm consuming 5 or 10Wh of energy every day which is close to nothing and probably sustainable with a solar panel.
Every once in a while (basically when the SD is almost full) I transfer the files with rclone to an external drive where I consolidate the files.
Oh extra tip, with rclone you can create a DLNA server so you can serve the files you have download immediately (tested with VNC and Kodi)
The phone/server has still room (CPU & RAM) to go and possibly I could install HomeAssistant without any issue. Also I could add Joplin and Floccus using webdav for storage as I had in my previous server but I don't miss them.
Any other questions, doubts, scripts, feel free to ask!
Haven't really tinkered with anything similar to be honest, but it should be doable. Figure out your software stack, find the lowest power consuming platform you can afford with enough performance to meet your needs, then power it with whatever green energy you can get. There are many commercial solutions for solar+battery combination.
My approach would be a raspberry pi, a power bank and a usb solar panel, I'm curious what kind of experience it would provide.