feat(coding-agent): add timeout option to extension dialogs with live countdown

Extension UI dialogs (select, confirm, input) now support a timeout option
that auto-dismisses with a live countdown display. Simpler alternative to
manually managing AbortSignal for timed dialogs.

Also adds ExtensionUIDialogOptions type export and updates RPC mode to
forward timeout to clients.

packages/coding-agent/src/modes/interactive/components/countdown-timer.ts

@@ -0,0 +1,38 @@
+/**
+ * Reusable countdown timer for dialog components.
+ */
+
+import type { TUI } from "@mariozechner/pi-tui";
+
+export class CountdownTimer {
+	private intervalId: ReturnType<typeof setInterval> | undefined;
+	private remainingSeconds: number;
+
+	constructor(
+		timeoutMs: number,
+		private tui: TUI | undefined,
+		private onTick: (seconds: number) => void,
+		private onExpire: () => void,
+	) {
+		this.remainingSeconds = Math.ceil(timeoutMs / 1000);
+		this.onTick(this.remainingSeconds);
+
+		this.intervalId = setInterval(() => {
+			this.remainingSeconds--;
+			this.onTick(this.remainingSeconds);
+			this.tui?.requestRender();
+
+			if (this.remainingSeconds <= 0) {
+				this.dispose();
+				this.onExpire();
+			}
+		}, 1000);
+	}
+
+	dispose(): void {
+		if (this.intervalId) {
+			clearInterval(this.intervalId);
+			this.intervalId = undefined;
+		}
+	}
+}