No, zero mouse usage, you can both address each tab by number and just moving between them. I wouldn't have any terminal emulator without the latter feature at least, and all I've tried support it.
Been a long time since I last tried tmux but was not switching between panes something like Ctrl-B + Ctrl-<something_else>? I don't remember but if it was that it's still much more than Super-Left/Right.
