Currently webpush notification method involves the call of the \phpbb\notification\method\messenger_base::is_available() method to determine webpush method availability for notification types.

messenger_base::is_available() relies on availability of email templates (email templates aren't used by webpush notification method though). So currently if some [custom] notification has no email templates for some reason, corresponding webpush method checkbox is disabled in notification types list.

Suggestion is to drop this dependency just like for the board notification method which also don't need email templates to work.