Replace tab.ActivePaneChanged handler with a method (#17331)

I noticed this while working on #17330. We're constructing a whole
lambda just to do this wacky weak_ref logic, and that feels... gross. We
should just make this a bound method and a typed event, so we can just
use the one event handler regardless

src/cascadia/TerminalApp/TabManagement.cpp

@@ -136,26 +136,7 @@ namespace winrt::TerminalApp::implementation
         // When the tab's active pane changes, we'll want to lookup a new icon
         // for it. The Title change will be propagated upwards through the tab's
         // PropertyChanged event handler.
-        newTabImpl->ActivePaneChanged([weakTab, weakThis{ get_weak() }]() {
-            auto page{ weakThis.get() };
-            auto tab{ weakTab.get() };
-
-            if (page && tab)
-            {
-                // Possibly update the icon of the tab.
-                page->_UpdateTabIcon(*tab);
-
-                page->_updateThemeColors();
-
-                // Update the taskbar progress as well. We'll raise our own
-                // SetTaskbarProgress event here, to get tell the hosting
-                // application to re-query this value from us.
-                page->SetTaskbarProgress.raise(*page, nullptr);
-
-                auto profile = tab->GetFocusedProfile();
-                page->_UpdateBackground(profile);
-            }
-        });
+        newTabImpl->ActivePaneChanged({ get_weak(), &TerminalPage::_activePaneChanged });
 
         // The RaiseVisualBell event has been bubbled up to here from the pane,
         // the next part of the chain is bubbling up to app logic, which will

src/cascadia/TerminalApp/TerminalPage.cpp

@@ -2237,6 +2237,29 @@ namespace winrt::TerminalApp::implementation
         return true;
     }
 
+    // When the tab's active pane changes, we'll want to lookup a new icon
+    // for it. The Title change will be propagated upwards through the tab's
+    // PropertyChanged event handler.
+    void TerminalPage::_activePaneChanged(winrt::TerminalApp::TerminalTab sender,
+                                          Windows::Foundation::IInspectable args)
+    {
+        if (const auto tab{ _GetTerminalTabImpl(sender) })
+        {
+            // Possibly update the icon of the tab.
+            _UpdateTabIcon(*tab);
+
+            _updateThemeColors();
+
+            // Update the taskbar progress as well. We'll raise our own
+            // SetTaskbarProgress event here, to get tell the hosting
+            // application to re-query this value from us.
+            SetTaskbarProgress.raise(*this, nullptr);
+
+            auto profile = tab->GetFocusedProfile();
+            _UpdateBackground(profile);
+        }
+    }
+
     uint32_t TerminalPage::NumberOfTabs() const
     {
         return _tabs.Size();

src/cascadia/TerminalApp/TerminalPage.h

@@ -542,6 +542,8 @@ namespace winrt::TerminalApp::implementation
         winrt::Microsoft::Terminal::Control::TermControl _senderOrActiveControl(const winrt::Windows::Foundation::IInspectable& sender);
         winrt::com_ptr<TerminalTab> _senderOrFocusedTab(const IInspectable& sender);
 
+        void _activePaneChanged(winrt::TerminalApp::TerminalTab tab, Windows::Foundation::IInspectable args);
+
 #pragma region ActionHandlers
         // These are all defined in AppActionHandlers.cpp
 #define ON_ALL_ACTIONS(action) DECLARE_ACTION_HANDLER(action);

src/cascadia/TerminalApp/TerminalTab.cpp

@@ -1242,7 +1242,7 @@ namespace winrt::TerminalApp::implementation
         _RecalculateAndApplyReadOnly();
 
         // Raise our own ActivePaneChanged event.
-        ActivePaneChanged.raise();
+        ActivePaneChanged.raise(*this, nullptr);
     }
 
     // Method Description:

src/cascadia/TerminalApp/TerminalTab.h

@@ -99,7 +99,7 @@ namespace winrt::TerminalApp::implementation
 
         til::typed_event<TerminalApp::TerminalPaneContent> RestartTerminalRequested;
 
-        til::event<winrt::delegate<>> ActivePaneChanged;
+        til::typed_event<TerminalApp::TerminalTab, IInspectable> ActivePaneChanged;
         til::event<winrt::delegate<>> TabRaiseVisualBell;
         til::typed_event<IInspectable, IInspectable> TaskbarProgressChanged;