fix(claude): handle async background task notifications in remote mode

[xyzhang626]

Summary

• Fix Claude remote session blocking on async background task notifications (e.g. delayed responses from "say hi after 10 secs")
• The stream reader was blocking on pendingNextInput even when async task results arrived, causing notifications to be silently dropped

Problem

When Claude executes a background task (e.g. say hi after 10 secs), the task notification arrives asynchronously after the main response completes. The remote stream handler was waiting for pendingNextInput to resolve before processing new messages, which caused these async notifications to never be delivered to the user.

Reproduce

1. Start a Claude session in remote mode
2. Send: "say hi after 10 secs"
3. Before this fix: the delayed message is silently dropped
4. After this fix: the delayed message is correctly delivered

Changes

• claudeRemote.ts: Refactor stream processing to not block on pendingNextInput when async task results arrive. Add debug traces for task notification lifecycle.
• claudeRemoteLauncher.ts: Add debug logging for incoming messages in the launcher bridge.
• claudeRemote.test.ts: Add test cases covering the async notification flow.

Test plan

• Run bun test claudeRemote.test.ts
• Start a remote Claude session, send "say hi after 10 secs", verify the delayed message arrives
• Verify normal synchronous message flow is unaffected

[github-actions]

Review mode: initial

Findings: 1 major. See inline comment.

Testing: Not run (automation)

[github-actions]

[MAJOR] Unhandled rejection risk from fire-and-forget nextMessage. Detached async call has no catch, so any rejection bypasses the outer try/catch and becomes unhandled. Evidence: cli/src/claude/claudeRemote.ts:190.

Suggested fix:

        void (async () => {
            try {
                const next = await opts.nextMessage();
                if (!next) {
                    inputEnded = true;
                    messages.end();
                    logger.debug(
                        `${debugPrefix} nextMessage resolved null fetchId=${fetchId} elapsedMs=${Date.now() - startedAt}; input ended`
                    );
                    return;
                }
                mode = next.mode;
                messages.push({ type: 'user', message: { role: 'user', content: next.message } });
                logger.debug(
                    `${debugPrefix} nextMessage resolved fetchId=${fetchId} elapsedMs=${Date.now() - startedAt} ` +
                    `messageLength=${next.message.length} permissionMode=${next.mode.permissionMode}`
                );
            } catch (e) {
                inputEnded = true;
                messages.end();
                logger.debug(`${debugPrefix} nextMessage error fetchId=${fetchId}`, e);
            } finally {
                nextMessageFetchInFlight = false;
                logger.debug(`${debugPrefix} scheduleNextMessage done fetchId=${fetchId}`);
            }
        })();

[github-actions]

Review mode: initial
No issues found in modified lines.
Residual risk: tests not run in this review.
Testing: Not run (automation).