Hyperlinks refers to "OSC 8" which is an escape code for making clickable links. for GNU Screen (released versions in my distro) this is an unknown escape and is stripped, tmux "passes it on" to the surrounding terminal and it is then usable.
Programs such as GNU coreutils ls (ls --hyperlink=always) can use hyperlink escapes in the outputs to make every file name it lists clickable, for example.
Of course there are ways to escape these escapes and get them to pass through screen - I wrote an escape code script myself to do it - but that experience is still inferior to native support, which tmux has nowadays.
Well I used GNU screen for a long time but it finally broke through now due to truecolor, and I managed to switch :)
I tested both zellij and tmux before switching, I was considering zellij as the first alternative. But zellij had some noticeable performance problems compared to tmux when it comes to throughput of terminal output, so I picked tmux.
My virtual terminal (iTerm2, Alacritty) makes mouse-clicking a link opens it in Firefox.
I've used GNU screen for 25 years. I gave tmux a try 10-15 years ago, but I didn't see the upside.
I'm curious about Zellij and its wasm plugins, but equally skeptical.
All I ever do in screen is ^A D, ^A C, ^A SPC, not sure what else I need?