Claude Code stopped working in tmux for me at some point. Which is of course more of a CC problem than a tmux one, but maybe OP was trying to work around such issues.
No idea what your problem is but this is categorically false. CC broke tmux when they briefly tried to open subagents inside their own tmux sessions but they've since resolved it. But they do take over the mouse mode I think.
cc works fine for me in tmux. there is also the `/tui` command that will change the behavior of the harness from one that intercepts scrolling etc (they call this fullscreen) and the default. I run mine in default mode.