F13-F24 are definitely valid keyboard codes, but I suspect that they weren't bothered with in Darkplaces (or possibly in your operating system).
First, check your OS supports it.
If you haven't selected the keyboard properly (ie: you selected a generic 101/105 key keyboard and never changed it) then it hasn't been told to support it. You either need to select the right keyboard, or go through and add in the extra functionality yourself by changing the config or hacking it to work.
In Linux, there's heaps of tools and many have changed over time. The latest is setxkbmap (within X), but tools like xev (within X) and showkey (outside of X) are useful for finding the keycode so you can map it properly to the right option.
This doesn't mean Darkplaces will work after that (may still be a problem there), but it does mean a dev running Linux could map a key on their keyboard to F13-F24 to test if it's just keyboard mapping or if Darkplaces has an issue.
FWIW: You can remap any key usually, so you could remap the Windows and Menu keys, or any extra keys your gaming keyboard has to these function keys. Just make sure all your normal keys work afterwards, as some keyboard that have extra keys simply send the same keycode as other keys on the keyboard (so you can't remap them without breaking those other keys as well - eg: some keyboards with duplicate rows of F keys that run vertically next to the keyboard, as well as the ones that run over the top).
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