What you're looking for is Jellyfin + Sonarr (TV Shows) + Radarr (Movies), you can also add more optionals like Bazarr (Subtitles) etc. (they're called the 'arr' programs).
Easiest way to set this up is a Docker container for each app and then configure them and connect them together through the UI. There's also an .ISO for normies called Umbrel that makes it look like an App Store if you can't be arsed to set up a home-server yourself.