At a generic system level, for example upgrading Nixos will pull new packages and put them next to the current ones, then reexec where possible. Nginx can replace its master process (SIGUSR2). Telephony software can often reexec and keep connecting open. Etc.

Outside of desktops it's not that uncommon to do seamless live reloads of the whole system.

Also out of superstition, I avoid hibernate -- when I walk away, it's either on and locked or shutdown. (I also did this on Windows; a mixed state just seemed off-puttingly and worryingly complex to me.)

Given what you said, and because I hear hibernation is notoriously buggy on Linux, both superstitions have rewarded me. :D

That's a pretty broad generalisation. Which distro's are you meaning?