I didn't see any way to use function keys in the session manager.
It would be really nice to be able to set any function key, with of course any modifier or combination of modifiers (shift-, ctrl-, alt-).
A function key value could be an arbitrary string that might or might not have embedded or trailing newlines.
If it had no newline, then it could be used to start part of a delayed line text, to be finished and entered to run manually.
If it has a trailing newline, then it could be used to enter and run a command (like a system command).
If it has any embedded newlines and a trailing newline, then it could be used to enter and run more than one command.
If it has embedded newlines but no trailing newline, then it could be used to enter and run a command, and then also submit a delayed line.