Quick update;
OK, so the addon started working after restarting the game. I was trying to debug using /reloadui earlier, while tinkering with the code. I didn't make any changes since posting this thread but it seems to work now:
https://ibb.co/M56wyqg
However, I think there are still some problems with Initialize() or event-calling logic in my code, as the GUI doesn't populate number of lockpicks until CountIncrement() is called by the EVENT_LOCKPICK_SUCCESS register.