feat(doctor): add linked-panes check for tmux session crosstalk (gt-uohw)

Detects when multiple gt-* tmux sessions share the same pane,
which causes messages sent to one session to appear in another.

This catches the bug where gt-deacon and gt-mayor shared a pane,
causing daemon heartbeats to appear as user input in the Mayor.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/cmd/doctor.go

@@ -61,6 +61,7 @@ func runDoctor(cmd *cobra.Command, args []string) error {
 	d.Register(doctor.NewBranchCheck())
 	d.Register(doctor.NewBeadsSyncOrphanCheck())
 	d.Register(doctor.NewIdentityCollisionCheck())
+	d.Register(doctor.NewLinkedPaneCheck())
 	d.Register(doctor.NewThemeCheck())
 
 	// Wisp storage checks