I am told that it's a restricted setting and "For your security, this setting is currently unavailable".
Since Android 13, the notification listener APIs are restricted to apps installed via a session-based package installer (the modern package management API for app stores): https://blog.esper.io/android-13-deep-dive/#restricted_settings_appop. If you installed it from an APK or from a store using legacy APIs like F-Droid, you'll need to go out of your way to allow notification access. From the linked article:
The user can then go to the app info settings for the app in question, open the menu, and then press “allow restricted settings” to unblock access to the app’s accessibility service.
It says "accessibility service" but this also applies to the notification listener APIs.
Of course the other option is to install Gadgetbridge from a proper store using the modern package management API.