feat(ui): add reusable inherited-source badge control

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

src/ClaudeDo.Ui/Views/Controls/InheritedBadge.axaml

@@ -0,0 +1,13 @@
+<UserControl xmlns="https://github.com/avaloniaui"
+             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
+             x:Class="ClaudeDo.Ui.Views.Controls.InheritedBadge"
+             x:Name="Root">
+  <Border Background="{DynamicResource Surface3Brush}"
+          CornerRadius="4" Padding="6,1"
+          IsVisible="{Binding #Root.BadgeText, Converter={x:Static StringConverters.IsNotNullOrEmpty}}"
+          VerticalAlignment="Center" HorizontalAlignment="Left">
+    <TextBlock FontSize="11"
+               Foreground="{DynamicResource TextMuteBrush}"
+               Text="{Binding #Root.BadgeText}"/>
+  </Border>
+</UserControl>

src/ClaudeDo.Ui/Views/Controls/InheritedBadge.axaml.cs

@@ -0,0 +1,18 @@
+using Avalonia;
+using Avalonia.Controls;
+
+namespace ClaudeDo.Ui.Views.Controls;
+
+public partial class InheritedBadge : UserControl
+{
+    public static readonly StyledProperty<string?> BadgeTextProperty =
+        AvaloniaProperty.Register<InheritedBadge, string?>(nameof(BadgeText));
+
+    public string? BadgeText
+    {
+        get => GetValue(BadgeTextProperty);
+        set => SetValue(BadgeTextProperty, value);
+    }
+
+    public InheritedBadge() => InitializeComponent();
+}