feat(agent): added non-interrupting aside message support

- Added a new aside-message source on `Agent` and exposed it in `AgentLoopConfig` as `getAsideMessages`.
- Updated the agent loop to poll aside messages after tool batches and before yielding, merging them with follow-up messages before continuing.
- Changed coding-agent session and yield queue handling to pull queued background messages via `drainMessages` at step boundaries instead of streaming-only injection.

packages/coding-agent/src/session/yield-queue.ts

@@ -10,7 +10,7 @@ export interface YieldDispatcher<P> {
 
 export interface YieldQueueOptions {
 	isStreaming: () => boolean;
-	injectStreaming(msg: AgentMessage): void;
+	injectStreaming?(msg: AgentMessage): void;
 	injectIdle(messages: AgentMessage[]): Promise<void>;
 	scheduleIdleFlush(run: () => Promise<void>): void;
 }
@@ -85,7 +85,7 @@ export class YieldQueue {
 			if (!message) continue;
 			if (mode === "streaming") {
 				try {
-					this.#options.injectStreaming(message);
+					this.#options.injectStreaming?.(message);
 				} catch (error) {
 					logger.warn("Yield queue streaming dispatch failed", { kind, error: formatError(error) });
 				}
@@ -102,6 +102,24 @@ export class YieldQueue {
 		}
 	}
 
+	/**
+	 * Build and remove all queued messages, applying each dispatcher's staleness
+	 * filter. No injection side effects — used for pull-based delivery at agent
+	 * step boundaries (see `Agent.setAsideMessageProvider`), so background-job
+	 * completions and late diagnostics reach the model between requests without
+	 * the agent having to stop.
+	 */
+	drainMessages(): AgentMessage[] {
+		const messages: AgentMessage[] = [];
+		for (const [kind, dispatcher] of this.#dispatchers) {
+			const entries = this.#drain(kind);
+			if (entries.length === 0) continue;
+			const message = this.#build(kind, dispatcher, entries);
+			if (message) messages.push(message);
+		}
+		return messages;
+	}
+
 	clear(): void {
 		this.#entries.clear();
 		this.#idleFlushPending = false;