hrvoje459 in the FriendsOfFlarum upload settings, next to each MIME type, there is a dropdown for how the file will be inserted in the post. That's what is called a "template" in this extension.
Some of the templates have the URL inserted as a bbcode parameter in the post body. Other templates retrieve the file URL based on the file ID which is inserted in the post body. Theoretically the second one should be able to update depending on the canonical URL, but in practice I think in the second case it's just using the pre-computed URL stored in the files table so it also won't update.
Officially neither Flarum nor this extension supports having multiple access URLs. There are probably solutions around this, like rewriting the URLs to be relative or using the TextFormatter extender to modify URLs on the fly as posts are retrieved, but they aren't built into the extension.
