Stabilize Windows UIA focus live gate

Tools/windows/uia-live-gate.ps1

@@ -1002,13 +1002,33 @@ try {
   # busy runner more headroom to let the app's own focus-reassertion converge.
   for ($index = 0; $index -lt 600; $index++) {
     $null = [GraphCodeUiaGateState]::ActivateWindow($shellWindow)
+    # A delayed, activation-driven refocus has been observed to re-target the workspace's Text
+    # Area shortly after ActivateWindow returns. Settle briefly so our SetFocus below lands after
+    # that reassertion, rather than being immediately overwritten by it before we sample focus.
+    Start-Sleep -Milliseconds 40
     $safeFocusRow.SetFocus()
-    Start-Sleep -Milliseconds 50
     $candidate = [System.Windows.Automation.AutomationElement]::FocusedElement
     if ($candidate.Current.AutomationId -eq $safeRowId) {
       $focused = $candidate
       break
     }
+    Start-Sleep -Milliseconds 10
+  }
+  if ($null -eq $focused) {
+    # Final bounded nudge: give the foreground transition a longer settle window than any single
+    # polling iteration above, reassert focus once more, and recheck before failing with
+    # diagnostic focus data. This does not change the overall ~30s budget of the loop above.
+    $null = [GraphCodeUiaGateState]::ActivateWindow($shellWindow)
+    Start-Sleep -Milliseconds 300
+    $safeFocusRow.SetFocus()
+    for ($index = 0; $index -lt 4; $index++) {
+      $candidate = [System.Windows.Automation.AutomationElement]::FocusedElement
+      if ($candidate.Current.AutomationId -eq $safeRowId) {
+        $focused = $candidate
+        break
+      }
+      Start-Sleep -Milliseconds 50
+    }
   }
   Require ($null -ne $focused) "worktree row could not retain focus against concurrent desktop focus changes; focused=$($candidate.Current.AutomationId):$($candidate.Current.Name)"
   Require ($focused.Current.AutomationId -eq $safeRowId) "focus source identity was '$($focused.Current.AutomationId)', expected '$safeRowId'"