feat: add mutable composite component lifecycle contract

- add generic child change events for dynamic composite components

- update runtime mount tracking to subscribe through the common contract

- cover third-party dynamic composite keybinding theme and context injection

test/TinyTUI.Tests/Runtime/TuiRuntimeInputListenerTests.cs

@@ -287,6 +287,39 @@ public sealed class TuiRuntimeInputListenerTests
         Assert.Equal(1, component.SetThemeCount);
     }
 
+    [Fact]
+    public void RuntimeInjectsSharedContextIntoDynamicMutableCompositeChildren()
+    {
+        var terminal = new TestTerminalSession();
+        var theme = new TestTheme("third-party-mutable");
+        var keybindings = KeybindingRegistry.CreateDefault();
+        keybindings.SetUserBinding(TuiKeybindings.InputSubmit, KeyNames.Tab);
+        using var runtime = new TuiRuntime(terminal, new DefaultInputParser(), new CountingRenderer(), keybindings, theme);
+        var composite = new ThirdPartyMutableComposite();
+        var input = new TinyTUI.Components.Input();
+        var themeComponent = new RecordingThemeComponent();
+        var contextComponent = new RecordingRuntimeContextComponent();
+        var submitted = false;
+
+        input.OnSubmitted = _ => submitted = true;
+        runtime.Add(composite);
+        runtime.SetFocus(input);
+
+        runtime.Start();
+        composite.Add(new ThirdPartyComposite(new Box(input), themeComponent, contextComponent));
+        terminal.Receive("\t");
+        composite.Remove(composite.Children[0]);
+
+        Assert.True(submitted);
+        Assert.Same(theme, themeComponent.Theme);
+        Assert.Equal(1, themeComponent.SetThemeCount);
+        Assert.Equal(1, contextComponent.MountedCount);
+        Assert.Equal(1, contextComponent.UnmountedCount);
+        Assert.Same(runtime, contextComponent.LastMountedContext?.Runtime);
+        Assert.Same(theme, contextComponent.LastMountedContext?.Theme);
+        Assert.Same(keybindings, contextComponent.LastMountedContext?.Keybindings);
+    }
+
     [Fact]
     public void RuntimeInjectedEditorKeybindingsReachAutocompleteList()
     {
@@ -618,6 +651,47 @@ public sealed class TuiRuntimeInputListenerTests
         public IEnumerable<IComponent> GetChildren() => Children;
     }
 
+    private sealed class ThirdPartyMutableComposite : IMutableCompositeComponent
+    {
+        private readonly List<IComponent> _children = [];
+
+        public event EventHandler<CompositeComponentChildChangedEventArgs>? ChildAdded;
+
+        public event EventHandler<CompositeComponentChildChangedEventArgs>? ChildRemoved;
+
+        public IReadOnlyList<IComponent> Children => _children;
+
+        public void Add(IComponent component)
+        {
+            _children.Add(component);
+            ChildAdded?.Invoke(this, new CompositeComponentChildChangedEventArgs(component));
+        }
+
+        public void Remove(IComponent component)
+        {
+            if (_children.Remove(component))
+                ChildRemoved?.Invoke(this, new CompositeComponentChildChangedEventArgs(component));
+        }
+
+        public IReadOnlyList<string> Render(int width)
+        {
+            var lines = new List<string>();
+
+            foreach (var child in _children)
+                lines.AddRange(child.Render(width));
+
+            return lines;
+        }
+
+        public void Invalidate()
+        {
+            foreach (var child in _children)
+                child.Invalidate();
+        }
+
+        public IEnumerable<IComponent> GetChildren() => _children;
+    }
+
     private sealed class TestTheme(string name) : ITuiTheme
     {
         public string Cursor => $"{name}> ";