"automatically saves all my shit" - define "all"? If truly EVERYTHING, you would need at least as much free space as already used, + some for the OS

"installs" - well, that's possible and has been done before, it's just that nobody bothers anymore because it's complicated, also because that implies automatic partitioning and bootloading which often sucks at least on Linux land

"easy/stable Linux" - well, if by "easy" you mean "it will never ever ever 4-th wall break and demonstrate that a computer isn't a Netflix vending machine" then none. Unlike on Windows, the 4-th wall breaks are meaningful, however. On Windows it just tells you "lol this won't work, you suck, go reinstall".