Implement full E2E, integration, component, and unit tests, and resolve all leftover tmux-to-herdr issues in UI and core scripts

.agents/skills/multi-agent-mux-ui/packages/mam_pty/lib/src/pty_session.dart

@@ -182,7 +182,9 @@ class PtySession {
       // A. Disassociate controlling terminal
       setsid();
 
-      // B. Isolate from nested TMUX environments (§6.7)
+      // B. Isolate from nested TMUX/Herdr environments (§6.7)
+      // We must unset TMUX and TMUX_PANE to ensure the child shell is properly isolated 
+      // from any parent terminal multiplexer session, preventing unexpected nested behavior.
       unsetenv(tmuxNamePtr.cast<ffi.Char>());
       unsetenv(tmuxPaneNamePtr.cast<ffi.Char>());