Note that you MUST have the video drive connected to the "home sharing" Mac for the files to play on AppleTV.
That's a very important point! I don't know if this has been fixed in the new Music and TV apps, but long ago had my library on an external drive and started the app once when the drive wasn't connected. It totally corrupted my library which took awhile to fix.
The problem was, even if you chose an external drive for the media itself, iTunes stored the library database in the default location on your internal drive. So, if you started iTunes without the external drive it completely confused the software (because it couldn't find the media files).
The fix was to manually copy the database file to the external drive and delete the original. In iTunes this was iTunes Library.itl, in the TV app (I think) would be TV Library.tvlibrary
Again, this was 10 years ago so maybe it's fixed now? I had actually forgotten about this when I moved my library from iTunes to the Music/TV apps a few weeks ago and should probably look into this again, since my library is on an external SSD!
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