Overseer/Jellyseer/Ombi are request interfaces. You and your users submit requests for movies/shows (music too if you use Lidarr) through there.
Those requests are fed into Sonarr/Radarr which actually manage the media files. They will search your indexers via Jackett/Prowlarr to find the most suitable torrent or nzb, dropping that into your download client (I use qbittorrent and SABnzbd, though I’ve disabled torrents for the time being.). Once completed Sonarr/Radarr will remove them from the download client, sort the files into your media folders and rename them accordingly. If a piece of media couldn’t be found, or is below your desired quality standard Sonarr/Radarr will monitor RSS feeds from your indexers and occasionally perform searches, upgrading files as they are found.
Finally Emby/Jellyfin/Plex can scan your media folders, grab metadata from imdb/thetvdb/themoviedb and present it all nicely for you.
If you haven’t already; putting these services behind a reverse proxy like nginx and a set of subdomains makes ease of use much better. Instead of remembering a bunch of port numbers and IPs: sonarr.domain.tld, radarr.domain.tld, etc.
Within my local network I run Pihole both to block most ads/tracking for every device on the local network, as well as just a local dns server to resolve those domains. (I also own a public domain to easily reach my stuff remotely)