Practically in this century if I was starting a new OS I would set it up like so:
/bin for all system binaries. Any binary from a package installed by the OS package manager lived here.
/lib same but for shared libraries
/var for variable data. This is where you would put things like your Postgres data files.
/tmp for temporary files.
/home as usual.
/dev as usual.
/boot as usual
/etc as usual
/usr would be what /usr/local is on most systems. So /usr/bin is binaries not installed by the OS package manager. /usr/etc is where you put config files for packages not installed by the package manager and so on.
Get rid of /usr/local and /sbin.
/media replaces /mnt entirely (or vice versa).
Ditch /opt and /srv
Add /sub for subsystems: container overlays should live here. This would allow the root user (or a docker group, etc.) to view the container file system, chroot into it, or run a container on it.
Then again, nobody gave me a PDP-11 to decide so my vote doesn’t count :)
I think that became the rationale for /[s]bin vs. /usr/[s]bin (although based on the linked article, that may have been retconned a bit).
You were supposed to keep your root/boot filesystem very small and mostly read-only outside major updates. That meant that you could boot to a small amount of utilities (e.g. fsck) that would let you repair /usr or any other volume if it became corrupted.
I think the other poster is correct that stuff like fsck is supposed to go into /sbin because it is a "system" binary (but also statically linked since /usr/lib isn't mounted yet) and doesn't make sense to have in user $PATHs since nobody other than root should really be running that one.
Regardless, this is all deeply meaningless these days, particularly if you are running "ephemeral" infrastructure where if anything goes that wrong you just repave it all and start over.