Fix some smaller broadcast bugs (#15993)

## Summary of the Pull Request

Resolves the following in #15812 

> - [x] `toggleBroadcastInput` isn't in the default settings
> - [x] The cursors forget to keep blinking if you focus each pane and
then unfocus them
> - [x] They don't stop blinking when you unbroadcast
> - [x] Broadcast border doesn't appear when you make new panes, but
they ARE broadcasted-to!

## References and Relevant Issues
x-ref:
* #2634
* #14393

## Detailed Description of the Pull Request / Additional comments

There was literally no logic in the original PR for starting the cursor
blinking. It's entirely unknowable how that ever worked. This makes it
all much more explicit.

We're taking the hacky `DisplayCursorWhileBlurred` from #15363, and
promoting that to the less-hacky `CursorVisibility`. Broadcast input
mode can use that to force the cursor to be visible always.


The last checkbox in that issue is harder, and I didn't want to further
pollute this delta with the paste plumbing.

src/cascadia/TerminalApp/Pane.cpp

@@ -2518,6 +2518,7 @@ std::pair<std::shared_ptr<Pane>, std::shared_ptr<Pane>> Pane::_Split(SplitDirect
         _profile = nullptr;
         _control = { nullptr };
         _firstChild->_isDefTermSession = _isDefTermSession;
+        _firstChild->_broadcastEnabled = _broadcastEnabled;
     }
 
     _splitState = actualSplitType;
@@ -3173,6 +3174,9 @@ void Pane::EnableBroadcast(bool enabled)
     if (_IsLeaf())
     {
         _broadcastEnabled = enabled;
+        _control.CursorVisibility(enabled ?
+                                      CursorDisplayState::Shown :
+                                      CursorDisplayState::Default);
         UpdateVisuals();
     }
     else

src/cascadia/TerminalApp/TerminalPage.cpp

@@ -4698,6 +4698,21 @@ namespace winrt::TerminalApp::implementation
         // the settings, change active panes, etc.
         _activated = activated;
         _updateThemeColors();
+
+        if (const auto& tab{ _GetFocusedTabImpl() })
+        {
+            if (tab->TabStatus().IsInputBroadcastActive())
+            {
+                tab->GetRootPane()->WalkTree([activated](const auto& p) {
+                    if (const auto& control{ p->GetTerminalControl() })
+                    {
+                        control.CursorVisibility(activated ?
+                                                     Microsoft::Terminal::Control::CursorDisplayState::Shown :
+                                                     Microsoft::Terminal::Control::CursorDisplayState::Default);
+                    }
+                });
+            }
+        }
     }
 
     winrt::fire_and_forget TerminalPage::_ControlCompletionsChangedHandler(const IInspectable sender,

src/cascadia/TerminalControl/TermControl.cpp

@@ -1051,8 +1051,8 @@ namespace winrt::Microsoft::Terminal::Control::implementation
             // _cursorTimer doesn't exist, and it would never turn on the
             // cursor. To mitigate, we'll initialize the cursor's 'on' state
             // with `_focused` here.
-            _core.CursorOn(_focused || DisplayCursorWhileBlurred);
-            if (DisplayCursorWhileBlurred)
+            _core.CursorOn(_focused || _displayCursorWhileBlurred());
+            if (_displayCursorWhileBlurred())
             {
                 _cursorTimer->Start();
             }
@@ -1968,7 +1968,7 @@ namespace winrt::Microsoft::Terminal::Control::implementation
             TSFInputControl().NotifyFocusLeave();
         }
 
-        if (_cursorTimer && !DisplayCursorWhileBlurred)
+        if (_cursorTimer && !_displayCursorWhileBlurred())
         {
             _cursorTimer->Stop();
             _core.CursorOn(false);
@@ -3660,4 +3660,45 @@ namespace winrt::Microsoft::Terminal::Control::implementation
         SelectionContextMenu().Hide();
         _core.ContextMenuSelectOutput();
     }
+
+    // Should the text cursor be displayed, even when the control isn't focused?
+    // n.b. "blur" is the opposite of "focus".
+    bool TermControl::_displayCursorWhileBlurred() const noexcept
+    {
+        return CursorVisibility() == Control::CursorDisplayState::Shown;
+    }
+    Control::CursorDisplayState TermControl::CursorVisibility() const noexcept
+    {
+        return _cursorVisibility;
+    }
+    void TermControl::CursorVisibility(Control::CursorDisplayState cursorVisibility)
+    {
+        _cursorVisibility = cursorVisibility;
+        if (!_initializedTerminal)
+        {
+            return;
+        }
+
+        if (_displayCursorWhileBlurred())
+        {
+            // If we should be ALWAYS displaying the cursor, turn it on and start blinking.
+            _core.CursorOn(true);
+            if (_cursorTimer.has_value())
+            {
+                _cursorTimer->Start();
+            }
+        }
+        else
+        {
+            // Otherwise, if we're unfocused, then turn the cursor off and stop
+            // blinking. (if we're focused, then we're already doing the right
+            // thing)
+            const auto focused = FocusState() != FocusState::Unfocused;
+            if (!focused && _cursorTimer.has_value())
+            {
+                _cursorTimer->Stop();
+            }
+            _core.CursorOn(focused);
+        }
+    }
 }

src/cascadia/TerminalControl/TermControl.h

@@ -160,6 +160,9 @@ namespace winrt::Microsoft::Terminal::Control::implementation
         TerminalConnection::ITerminalConnection Connection();
         void Connection(const TerminalConnection::ITerminalConnection& connection);
 
+        Control::CursorDisplayState CursorVisibility() const noexcept;
+        void CursorVisibility(Control::CursorDisplayState cursorVisibility);
+
         // -------------------------------- WinRT Events ---------------------------------
         // clang-format off
         WINRT_CALLBACK(PropertyChanged, Windows::UI::Xaml::Data::PropertyChangedEventHandler);
@@ -194,9 +197,6 @@ namespace winrt::Microsoft::Terminal::Control::implementation
 
         WINRT_OBSERVABLE_PROPERTY(winrt::Windows::UI::Xaml::Media::Brush, BackgroundBrush, _PropertyChangedHandlers, nullptr);
 
-    public:
-        til::property<bool> DisplayCursorWhileBlurred{ false };
-
     private:
         friend struct TermControlT<TermControl>; // friend our parent so it can bind private event handlers
 
@@ -258,6 +258,8 @@ namespace winrt::Microsoft::Terminal::Control::implementation
         Windows::Foundation::Collections::IObservableVector<Windows::UI::Xaml::Controls::ICommandBarElement> _originalSelectedPrimaryElements{ nullptr };
         Windows::Foundation::Collections::IObservableVector<Windows::UI::Xaml::Controls::ICommandBarElement> _originalSelectedSecondaryElements{ nullptr };
 
+        Control::CursorDisplayState _cursorVisibility{ Control::CursorDisplayState::Default };
+
         inline bool _IsClosing() const noexcept
         {
 #ifndef NDEBUG
@@ -376,6 +378,7 @@ namespace winrt::Microsoft::Terminal::Control::implementation
 
         void _SelectCommandHandler(const IInspectable& sender, const IInspectable& args);
         void _SelectOutputHandler(const IInspectable& sender, const IInspectable& args);
+        bool _displayCursorWhileBlurred() const noexcept;
 
         struct Revokers
         {

src/cascadia/TerminalControl/TermControl.idl

@@ -12,6 +12,12 @@ import "ControlCore.idl";
 namespace Microsoft.Terminal.Control
 {
 
+    enum CursorDisplayState
+    {
+        Default,
+        Shown
+    };
+
     [default_interface] runtimeclass TermControl : Windows.UI.Xaml.Controls.UserControl,
                                                    IDirectKeyListener,
                                                    IMouseWheelListener,
@@ -121,7 +127,7 @@ namespace Microsoft.Terminal.Control
         // opacity set by the settings should call this instead.
         Double BackgroundOpacity { get; };
 
-        Boolean DisplayCursorWhileBlurred;
+        CursorDisplayState CursorVisibility;
 
         Windows.UI.Xaml.Media.Brush BackgroundBrush { get; };
 

src/cascadia/TerminalSettingsEditor/Profiles_Appearance.cpp

@@ -41,7 +41,7 @@ namespace winrt::Microsoft::Terminal::Settings::Editor::implementation
             _previewControl = Control::TermControl(settings, settings, *_previewConnection);
             _previewControl.IsEnabled(false);
             _previewControl.AllowFocusWhenDisabled(false);
-            _previewControl.DisplayCursorWhileBlurred(true);
+            _previewControl.CursorVisibility(Microsoft::Terminal::Control::CursorDisplayState::Shown);
             ControlPreview().Child(_previewControl);
         }
 

src/cascadia/TerminalSettingsModel/defaults.json

@@ -437,6 +437,7 @@
         { "command": { "action": "swapPane", "direction": "previousInOrder"} },
         { "command": { "action": "swapPane", "direction": "nextInOrder"} },
         { "command": { "action": "swapPane", "direction": "first" } },
+        { "command": "toggleBroadcastInput" },
         { "command": "togglePaneZoom" },
         { "command": "toggleSplitOrientation" },
         { "command": "toggleReadOnlyMode" },