While remote authentication is the default, you can configure Plex to not require any sort of auth at all for local users. That’s how mine is setup, and we can watch content around the house even when our ISP is offline.
I also don’t get ads or anything else pushing other content - I only ever see my own. You just have to not show those things in the sidebar. So again, the defaults can be changed.
Definitely worth trying Jellyfin if it works for a particular case. I’ve tried Jellyfin, Emby, and Plex - but only found the latter to be reliable enough for OTA DVR via an HDHomeRun which is our primary use case.