Allow the entire Tab to be hit testable again (#11369)

DESPITE the fact that there's a `Background()` API that we
could just call like:

```c++
  TabViewItem().Background(deselectedTabBrush);
```

We actually can't, because it will make the part of the tab that
doesn't contain the text totally transparent to hit tests. So we
actually _do_ still need to set `TabViewItemHeaderBackground` manually.

* Regressed in #11240
* Root cause up in microsoft/microsoft-ui-xaml#3769
* [x] closes #11294

src/cascadia/TerminalApp/TerminalTab.cpp

@@ -1460,7 +1460,16 @@ namespace winrt::TerminalApp::implementation
         // TabViewItem().Background() only sets the color of the tab background
         // when the TabViewItem is unselected. So we still need to set the other
         // properties ourselves.
-        TabViewItem().Background(deselectedTabBrush);
+        //
+        // GH#11294: DESPITE the fact that there's a Background() API that we
+        // could just call like:
+        //
+        //     TabViewItem().Background(deselectedTabBrush);
+        //
+        // We actually can't, because it will make the part of the tab that
+        // doesn't contain the text totally transparent to hit tests. So we
+        // actually _do_ still need to set TabViewItemHeaderBackground manually.
+        TabViewItem().Resources().Insert(winrt::box_value(L"TabViewItemHeaderBackground"), deselectedTabBrush);
         TabViewItem().Resources().Insert(winrt::box_value(L"TabViewItemHeaderBackgroundSelected"), selectedTabBrush);
         TabViewItem().Resources().Insert(winrt::box_value(L"TabViewItemHeaderBackgroundPointerOver"), hoverTabBrush);
         TabViewItem().Resources().Insert(winrt::box_value(L"TabViewItemHeaderBackgroundPressed"), selectedTabBrush);
@@ -1506,6 +1515,7 @@ namespace winrt::TerminalApp::implementation
     void TerminalTab::_ClearTabBackgroundColor()
     {
         winrt::hstring keys[] = {
+            L"TabViewItemHeaderBackground",
             L"TabViewItemHeaderBackgroundSelected",
             L"TabViewItemHeaderBackgroundPointerOver",
             L"TabViewItemHeaderForeground",
@@ -1526,9 +1536,6 @@ namespace winrt::TerminalApp::implementation
             }
         }
 
-        // Clear out the Background.
-        TabViewItem().Background(nullptr);
-
         _RefreshVisualState();
         _colorCleared();
     }