As discussed in System-files under .mozilla/native-messaging-hosts I added a hook to copy the file to the system. The snap layouts would not make the file available to the browser, so I’m not sure how that would work.
There has been one vote on System-files under .mozilla/native-messaging-hosts, so it might be better to close this to avoid confusion.
EDIT: The other post is more clear about the necessary connections.
The file is in the snap and needs to be copied in /usr/lib/mozilla/native-messaging-hosts to be read by Firefox.