Could you say more about this? I took a look at this page and it seems to be mainly about having a window manager in a terminal: https://zellij.dev/about/
But I have a window manager, so all I ever want out of something like screen or tmux is a persistent remote session that survives network issues or me closing my laptop for a bit. Is that something that Zellij is better at?
In my experience? Yeah, Zellij's UX for session management vastly improves over that of screen and tmux, and it comes out of the box with much saner defaults. However, like tmux, it offers more than just session management, and also like tmux, it does it all while remaining rather small and performant.
Just try it and see if you like it. I've found that most of things I didn't like, mainly the default TUI borders and buttons, were far more easily reconfigured compared to tmux.