feat(web): support background task execution (similar to Claude Code Ctrl+B)

[hqhq1025]

Feature Request

Claude Code CLI supports pressing Ctrl+B to send the current task to the background, allowing users to continue working on other things while the agent processes the task. It would be great to have a similar capability in the HAPI web UI.

Desired Behavior

• While the agent is processing a message in a session, the user should be able to "background" the task
• The user can then switch to other sessions or start new conversations without waiting
• A visual indicator should show which sessions have background tasks running
• When the background task completes, the user should be notified (e.g., badge, toast, or browser notification)

Use Case

When working with multiple tasks, it's common to send a long-running request (e.g., large refactoring, code review) and want to work on something else while waiting. Currently, the user has to stay on the session page or manually navigate away and remember to check back.

Possible Implementation Ideas

• Add a "Send to background" button or keyboard shortcut in the session view
• Show a running task indicator in the session list sidebar
• Use browser notifications or an in-app notification system for task completion
• Persist the background state so it survives page refresh

[github-actions]

From the current code, HAPI already has part of this implemented, but not the full web workflow you described.

The hub already detects background-task start/completion signals from agent messages and updates a per-session backgroundTaskCount (hub/src/sync/backgroundTasks.ts:16, hub/src/sync/sessionCache.ts:250). In the web UI, that count is already shown inside the session chat status bar as N background task(s) running (web/src/components/AssistantChat/StatusBar.tsx:88, web/src/components/SessionChat.tsx:404).

What I did not find is the sidebar/session-list part yet. The summary shape used by the session list does not include backgroundTaskCount, and toSessionSummary() does not map it through (shared/src/sessionSummary.ts:13, shared/src/sessionSummary.ts:26). The current list item UI only renders active/thinking, todo progress, pending requests, and relative time (web/src/components/SessionList.tsx:396).

For notifications, there is already toast/push infrastructure in the web app, and the hub sends notifications for permission requests and ready events (hub/src/notifications/notificationHub.ts:57, hub/src/push/pushNotificationChannel.ts:57, web/src/App.tsx:157, web/src/hooks/usePushNotifications.ts:66, web/src/sw.ts:94). I did not find a notification path tied specifically to backgroundTaskCount reaching zero.

So current status from the codebase:

• Background task tracking: present
• In-session indicator: present
• Session-list background indicator: not found
• Background-task completion notification: not found

Relevant code:

• hub/src/sync/backgroundTasks.ts:16 - extracts background task start/completion deltas from agent messages
• hub/src/sync/sessionCache.ts:250 - applies backgroundTaskCount updates to the session cache and emits session-updated
• web/src/components/AssistantChat/StatusBar.tsx:88 - renders background task(s) running in the chat status bar
• shared/src/sessionSummary.ts:13 - session summary shape used by the sidebar does not include backgroundTaskCount
• web/src/components/SessionList.tsx:396 - session list item UI currently has no background-task indicator
• hub/src/notifications/notificationHub.ts:57 - notification hub reacts to ready events, not background-task completion

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HAPI Bot