How do I add a file that should allow me to use the .log to start the server?
You need to describe a bit more what you want to do.
inside the logs/latest.log section inside a mineos server has the option to run commands from the server console.
That being the case, there is a command to restart the world while running however the server will not restart when the command is used.
Unfortunately the command input in the log window in MineOS only support ingame related commands, so unless the server variant you use supports a restart command this is not possible.
Then you would need to add a script and a cron chekc to see if a server is running then start it if it has stopped. Then use the /stop command in the command input line, so it’ll really just be simpler to use the start and stop buttons in MineOS