To reproduce:

1. Use the FootSwitch app to configure your foot pedal to send F13 when pressed
2. Run VectorAudio, open settings, click Select New Key
3. Press the foot pedal

Result: VectorAudio appears to detect a key input, as the button reverts back to Select New Key, but the assigned key still shows as Unknown.
Expected result: F13 gets mapped as the PTT key

Screenshot from FootSwitch:

I am able to map F13 in Discord fine using a similar method (hit the Edit keybind button then press the foot pedal, it is detected properly by Discord).