Logitech G Hub - keys mapped to mouse buttons not sent to Discord

I have a Logitech G 403 Hero mouse where I configured mouse buttons 4 and 5 to send F16 and F19 when they are pressed. If I press these mouse buttons while in Terminal, I see the F keys outputs appearing there. I have F16 set to enable push to talk in Discord. However, when I press mouse button 4 to send F16, nothing happens in Discord.

Logitech G Hub Agent is enabled in both Privacy & Security / Accessibility and Privacy & Security / Input Monitoring.