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The TV part is easy - just connect it to a device that has HDMI output and can connect to and read from the NAS and the switch the TV input to HDMI. Personally I would suggest a Raspberry PiZero W - HDMI output & WiFi + Bluetooth: https://www.raspberrypi.org/products/raspberry-pi-zero-w/
Even with a case you are looking under £20.
Then you are just ...
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