In Apple TV there’s an option called ‘Computer’ where you can stream movies that are stored on your computer. But these movies need to be shared from your computer to Apple TV. In Catalina Apple changed how you turn this sharing on and off from your Computer.
Previously you need to go into iTunes and select ‘Turn on Home Sharing’ from your iTunes App. In Catalina it’s been moved from iTunes into the System Preferences. (It’s not been moved to the TV app – that’s where I went looking!)
To turn on sharing for your media Library you need to go into System Preferences, then ‘Sharing’ and then select the box that says ‘Media Sharing’ and then select the box that says ‘Home Sharing.’ Now all the movies that were in your old iTunes Library will be available on your Apple TV.
If you want to add files from a media server or external Hard Disk to be able to view them on your Apple TV as well, you can leave them in place on your media server but you need to drag them into the new TV app on your computer. Before you do this make sure you unselect the option that says ‘Copy files to media folder when adding to Library.’ If that box is selected it will try to copy your movies from your external drive to your computer’s internal drive, and fill it up. If you leave that box unchecked, it will make a link to your external movies (so that you can play them from Apple TV) but it will keep them on the media drive.