Can you explain what you struggle to do in tmux with the mouse? I'm using it as we speak and everything is clickable, panes are resizable, right clicking a windows give you a context menu... Not sure what else is missing?
I generally run a session per project. Then within each session, a window for Claude, a window for running whatever dev server/logs, a window for neovim, and finally a plain terminal window for things like kicking off deploys etc.
Anyway, I think multi-session management is a reasonable thing that this thing might improve over tmux, so fair enough.