This app was mentioned in 6 comments, with an average of 1.17 upvotes
They only have DS Video for Android TV
You could use Plex server on Synology + Plex client on Android TV to do what you want.
Or just use an app like ES File Explorer on Android TV to open the files off the NAS via the network and open with whatever app on the Android TV device.
it's about my Seinfeld Collection. I've ripped all my PAL DVDs. They are in my library. Each episode seperately. And I love the 4:3/90s feeling. But then I've got the High-Res MKVs recordings with another field of view (16:9)... I want both versions to be available via my Kodi-Library without getting double entries. (btw the synology app "DS VIDEO" can do this but sucks otherwise)
We have that functionality. Our video files are stored on a Synology DiskStation. We use the Android app, but you would want the iPhone/iPad version, to cast the videos to a Chromecast plugged into the TV. All of the artwork and info is by the server automatically and displayed on your phone/tablet in the app.
The Synology DiskStation has a bunch of additional functionality, but the most relevant to this discussion is the Download Station which can be used to manually or automatically download video files using FTP, HTTP, BitTorrent, NZB, etc.
If you're planning to have a Roku connected to the TV, you can also add the DS Video channel to your Roku and access the server directly from there.
You can do very similar things by using your own server to run Kodi or other software packages. I've been there and done that, and it's a complete pain in the rear compared to the Synology. If you want something for you to tinker around with, go for the roll-your-own solution. If you want something that's going to just work every time your wife wants to watch a show or movie, then get the Synology.
My DS1812+ is still working after a decade of 24/7 use with it's original power supply.
I lock the drive trays, like you're supposed to.
DS Video is still available:
You need "DS video", and you can find it here: https://play.google.com/store/apps/details?id=com.synology.dsvideo