Purchased movie on films and TV app only showing ascoming soon

could be your console needs to be reset

If you are talking of movies you have purchased from the Films & TV app, then you do not need to do anything, as the Xbox 360 and Windows 10 have their own Films & TV app, just log in on the device you want to watch those movies, and then launch the app.
Your movies should show.

If you have movies that you have purchased elsewhere and using the app to watch them. You only need to turn on the play to option on the xbox 360, then when you start the app on Windows 10, start a movie, then in the bottom corner of the film there will
three dots. Select it, and choose cast to device. The Xbox 360 should show up. select it, and it should play on your console.

The movies anywhere program only works for those United States, and only a material from member studios like Warner brothers, Sony, Disney and Universal and not for TV shows

Outside of a handful of theatrical films, no Japanese animation is a part of it

unfortunately, there is no mobile app for Microsoft movies and TV

You need to download the films & TV app on your Xbox. Then start the app, and your movies should show up for you to watch. https://www.microsoft.com/en-gb/p/films-tv/9wzdncrfj3p2?activetab=pivot:overviewtab

Hey there, so you're re-downloading previously purchased movies on to a new HDD? With TV shows and movies Unfortunately, you cannot transfer film and TV show licences from one console to another because of licensing restrictions.

So it looks like you only get 1 license per console. More information here:
support.xbox.com/.../download-content