docs: document Focusable interface propagation pattern for IME support

Container components with embedded Input/Editor children must implement
Focusable and propagate focus state to enable correct IME candidate
window positioning.

Related to #827

packages/coding-agent/docs/tui.md

@@ -52,6 +52,36 @@ When a `Focusable` component has focus, TUI:
 
 This enables IME candidate windows to appear at the correct position for CJK input methods. The `Editor` and `Input` built-in components already implement this interface.
 
+### Container Components with Embedded Inputs
+
+When a container component (dialog, selector, etc.) contains an `Input` or `Editor` child, the container must implement `Focusable` and propagate the focus state to the child. Otherwise, the hardware cursor won't be positioned correctly for IME input.
+
+```typescript
+import { Container, type Focusable, Input } from "@mariozechner/pi-tui";
+
+class SearchDialog extends Container implements Focusable {
+  private searchInput: Input;
+
+  // Focusable implementation - propagate to child input for IME cursor positioning
+  private _focused = false;
+  get focused(): boolean {
+    return this._focused;
+  }
+  set focused(value: boolean) {
+    this._focused = value;
+    this.searchInput.focused = value;
+  }
+
+  constructor() {
+    super();
+    this.searchInput = new Input();
+    this.addChild(this.searchInput);
+  }
+}
+```
+
+Without this propagation, typing with an IME (Chinese, Japanese, Korean, etc.) will show the candidate window in the wrong position on screen.
+
 ## Using Components
 
 **In hooks** via `ctx.ui.custom()`:

packages/tui/README.md

@@ -136,6 +136,58 @@ interface Component {
 
 The TUI appends a full SGR reset and OSC 8 reset at the end of each rendered line. Styles do not carry across lines. If you emit multi-line text with styling, reapply styles per line or use `wrapTextWithAnsi()` so styles are preserved for each wrapped line.
 
+### Focusable Interface (IME Support)
+
+Components that display a text cursor and need IME (Input Method Editor) support should implement the `Focusable` interface:
+
+```typescript
+import { CURSOR_MARKER, type Component, type Focusable } from "@mariozechner/pi-tui";
+
+class MyInput implements Component, Focusable {
+  focused: boolean = false;  // Set by TUI when focus changes
+  
+  render(width: number): string[] {
+    const marker = this.focused ? CURSOR_MARKER : "";
+    // Emit marker right before the fake cursor
+    return [`> ${beforeCursor}${marker}\x1b[7m${atCursor}\x1b[27m${afterCursor}`];
+  }
+}
+```
+
+When a `Focusable` component has focus, TUI:
+1. Sets `focused = true` on the component
+2. Scans rendered output for `CURSOR_MARKER` (a zero-width APC escape sequence)
+3. Positions the hardware terminal cursor at that location
+4. Shows the hardware cursor
+
+This enables IME candidate windows to appear at the correct position for CJK input methods. The `Editor` and `Input` built-in components already implement this interface.
+
+**Container components with embedded inputs:** When a container component (dialog, selector, etc.) contains an `Input` or `Editor` child, the container must implement `Focusable` and propagate the focus state to the child:
+
+```typescript
+import { Container, type Focusable, Input } from "@mariozechner/pi-tui";
+
+class SearchDialog extends Container implements Focusable {
+  private searchInput: Input;
+
+  // Propagate focus to child input for IME cursor positioning
+  private _focused = false;
+  get focused(): boolean { return this._focused; }
+  set focused(value: boolean) {
+    this._focused = value;
+    this.searchInput.focused = value;
+  }
+
+  constructor() {
+    super();
+    this.searchInput = new Input();
+    this.addChild(this.searchInput);
+  }
+}
+```
+
+Without this propagation, typing with an IME (Chinese, Japanese, Korean, etc.) will show the candidate window in the wrong position.
+
 ## Built-in Components
 
 ### Container