Let me try to explain this again.
The way OBS's hotkey system works is that OBS has a list of all the things internally that can be hotkeyed. Plugins can add new hotkeys to this list by registering a hotkey with OBS. They do this by calling the obs_hotkey_register function for the corresponding plugin type. For example, sources can register hotkeys using obs_hotkey_register_source().
Here is an example in the slideshow source.
The Automatic Scene Switcher is a frontend tool, so it uses obs_hotkey_register_frontend().
Here is an example where the transition hotkeys are defined.
The Settings window then takes all these hotkeys and automatically lays them out in the corresponding sections.
So you don't need to edit the hotkeys UI, you just need to register a hotkey in the automatic scene switcher itself.