Back to the days I was fixing a lot of computers of friends and relatives, my Swiss army knife of Linux was https://www.system-rescue.org/
Very lightweight but with a full set of recovery tools. I've tried it recently and I still find it up to the expectations.
I've also used a fair amount of https://clonezilla.org/ to (re)store images of freshly installed OSes (mostly windows XP and 7 to give you an idea of the timeframe) for people who I know would have messed up faster.
I did some experiments in the past. The nicer option I could find was enabling webdav API on the hosting side (it was an option on cPanel if I recall correctly, but there are likely other ways to do it). These allow using the webserver as a remote read/write filesystem. After you can use rclone to transfer files, the nice part is that rclone supports client side encryption so you don't have to worry too much about other people accessing files.