Streaming (e.g., Plex or Jellyfin or some UPnP server) helps you send the data to the TV client over the network from a remote server.
As you want to bring the data server right to the TV, and you'll output the video via HDMI, just use any PC. There are plenty of them designed for this (usually they're fanless for reducing noise)... search "home theater PC."
You can install Kodi as the interface/organizer for playing your media files. It handles the all the formats... the TV is just the ouput.
A USB CEC adapter will also allow you to use your TV remote with Kodi.