How can one resume an interrupted ffmpeg job or pause by design and save some kind of state file?
Depending on what shell you're using you can suspend a process (in posix shells it's with ctrlz, in Powershell you might use suspend-Job) and then resume it. This is true for any shell with job control. You can't quit and save the state from ffmpeg though.
A workaround would be to run the ffmpeg process in a virtual machine. Most linux distros have a minimal server version that would work for this. This would let you save the machine state, and restart the encode at a later date.