I did several tests with notifications in Thundebird, and I came to the dramatic conclusion that the notifications don’t work consistently with the Thunderbird Add-In.
As workaround I am adding all Calendars over CalDAV as read-only, just to get the working notifications from Thunderbird Lightning (and to integrate the today pane). This is only because our support partner told us we are not allowed to use CalDAV with Thunderbird.
I activated the debug logs in the Add-In but only these rows looked relevant:
[INFO ][2024-11-21T14:10:22.313Z]Console: [JavaScript Error: "The Notification permission may only be requested from inside a short running user-generated event handler." {file: "<CENSORED URL>/cal/iframe.html" line: 0}]
[INFO ][2024-11-21T14:10:32.058Z]Console: [JavaScript Error: "TypeError: calTab[0] is undefined" {file: "moz-extension://<CENSORED UUID>/background.js" line: 116}]