

For Debian there’s Preseed, for Arch there’s archinstall, for a Fedora/RHEL there’s Kickstart, for Alpine there’s setup scripts, for distros with fully manual installs, you could just write a script?
Automating your install is something any sysadmin and mainly any distro developer will quickly reach towards, so it is something almost certain to exist.
Though, if I understand you, you’d want that to be “sourced” from an existing system, yes? I can see the use of that… NixOS is likely the closest to what you want, since you are always defining a full declaration of your system.
That’s the best, safest way. By the way, you can do the same thing from a flash drive too, if it has enough space to hold the system. I don’t mean as a live temporary system, I mean you can just point the installer to a second flash drive as the install disk and it won’t care.