They are not in the same continuity. Warner Brothers controls the Jackson films and has their own cinematic universe that they are still creating things for. The Video games and soon to be Anime are part of the WB "universe". Amazon has their own now and even has rights to create spinoffs from Rings of Power. Neither are required to honor each other. Obviously some things from Amazon will look similar because Tolkien being the source and using popular imagery the Jackson films had.
I doubt it is something the Tolkien estate would include since they didn't like how Netflix wanted to do a MCU. They pitched a Gandalf show, an Aragorn drama, and likely more.