What exactly pressing <F13> sends?

I have <Eject> key mapped to <F13> with Karabiner-Elements. And if tested in Terminal.app or Alacritty.app, it correctly reports ^[[25~

However, in MacVim, if I :terminal cat, and then press <F11>, <F12> and then <F13>, I see ^[[23~, ^[[24~, and then just some sort of space (the cursor moves one position to the right, while reporting nothing):

It does work OK, though, I can create mappings with <F13>. But if I use some TUI application in :terminal, then it clearly doesn't understand it.

:set t_F3 or :set <F13> both report E846: Key code not set. Trying to actually set those to ^[[25~ makes no effect (:terminal cat still reports that mysterious space). Reproducible on the latest release.

Any hints may be? :)

Well, tnoremap <F13> ^[[25~ seems to solve the problem :). But still, what exactly does it send by default?

Reproduce the issue in MacVim with :terminal cat, comparing F11, F12, and F13 against Terminal.app or Alacritty.app. Investigate how MacVim handles F13 in the embedded terminal and verify whether tnoremap ^[[25~ changes the result; done means identifying the default sequence or correcting the discrepancy.