feat(stream): TASK 41 Test Stream mode — private test broadcast + TEST drawer

Test button next to Start runs the real private-only go-live pipeline as a
session variant (IsTestStream): BeginTestStream -> extracted
StartStreamingSession(alsoRecord:false) shared with the dialog path — no Go
Live dialog, no 'last live' stamp, no recording. Gold top bar + TEST badge +
'End Test' button face; TEST drawer (third right-rail pull-out, three-way
exclusivity) auto-opens once the liveChatId resolves.

Chat tooling: Mock Chat Input sends a REAL liveChat/messages.insert
(YouTubeStreamService.InsertChatMessageAsync) that round-trips the real ~2s
poll and renders through the live overlay; simulated Subscriber/New
Member/Super Chat events inject through the poller's MessageReceived seam
(YouTubeChatService.InjectSimulatedMessage, ChatMessage.IsSimulated) — the
insert API only creates textMessageEvent, so non-text events are local-only
by design (ref: developers.google.com/youtube/v3/live/docs/liveChatMessages/insert).
Scopes youtube + youtube.force-ssl already cover insert; no re-consent.

Good Dog: ytLive.Tests/TestStreamTests.cs — coordinator protocol with fake
HTTP + real-window drawer exclusivity/gate. 0 warnings; 314/314 pass (clean
run; intermittent host abort is the pre-existing WinRT-webcam flake).

Docs ride in the same change: TASKS.md row 41, TASKS/task-41-test-stream-mode.md,
ai.md (YouTube Live API constraints), HANDOFF rewrite.

Controls/TopBar.xaml

@@ -58,6 +58,11 @@
             <TextBlock Text="{Binding LiveElapsedText}" Foreground="White" FontSize="14"
                        FontFamily="Consolas" VerticalAlignment="Center" Margin="14,0,0,0"
                        Visibility="{Binding IsLive, Converter={StaticResource BoolToVis}}"/>
+            <Border Background="#9c6f1c" CornerRadius="3" Padding="6,1" Margin="10,0,0,0"
+                    VerticalAlignment="Center"
+                    Visibility="{Binding IsTestStream, Converter={StaticResource BoolToVis}}">
+                <TextBlock Text="TEST" FontSize="11" FontWeight="Bold" Foreground="White"/>
+            </Border>
         </StackPanel>
 
         <!-- Three-state top bar: logged-out / idle / live -->
@@ -92,6 +97,14 @@
                                Visibility="Collapsed"/>
                 </Grid>
             </Border>
+            <!-- Test button (TASK 41): one-click private test broadcast — the Test
+                 drawer (right rail, TEST tab) hosts the mock chat input + simulated
+                 events. Visible only signed-in and idle. -->
+            <Button Content="Test" Style="{StaticResource YtButtonSecondary}" Padding="12,4" FontSize="11"
+                    Margin="0,0,8,0" VerticalAlignment="Center"
+                    Command="{Binding StartTestCommand}"
+                    ToolTip="Start a private test broadcast to check your chat overlay and chat tools."
+                    Visibility="{Binding ShowTestButton, Converter={StaticResource BoolToVis}}"/>
             <!-- Primary Start button: the always-present idle action (sign-in moved
                  into its context menu — a bare bar after stopping was a dead end) -->
             <Button Content="{Binding PrimaryStartButtonLabel}" Style="{StaticResource YtButton}"