Plex

So that is when you have Managed Accounts. People in your house and subnet can access plex without having to log in. They just pop up and click on their account to watch. When the internet is out, what I noticed is that every device on the subnet was only able to select the Home Admin account, so individual selection of Managed Accounts was not available when you couldn't reach the Plex mothership for authentication. Not completely unusable, but it wasn't ideal. If OP wanted to use Managed Accounts, that's not going to be possible with no internet. But with Jellyfin, it doesn't need that to have managed accounts. I had Plex and Jellyfin running on a VM at one point, and was able to switch between the two so that I could keep both libraries up to date. I switched to a dedicated machine and haven't put Jellyfin back on, but that is another solution for OP, just have both loaded on the machine, and use whichever one is best for them at the time.