[Cowork/Dispatch] Remote approval for Mac dialogs with mobile push notifications

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Problem 1 — Dialogs require physical presence
When Cowork's request_access triggers a native macOS permission dialog, the user must be physically at their Mac to approve within the 60-second timeout. Users who are away (traveling, on a flight) cannot approve, blocking all computer-use tasks for the entire remote session.

Problem 2 — No push notification for Dispatch messages
Even if approval requests were forwarded to Dispatch, the Claude mobile app currently has no push notification mechanism. Users only see Dispatch messages if they already have the app open — making remote approval impractical.

Proposed Solution

1. Forward request_access dialogs to the Dispatch text channel as interactive messages with Approve/Deny buttons
2. Send a push notification to the user's mobile device (iOS/Android) when a Dispatch approval request is pending
3. Relay the user's response back to dismiss the dialog on Mac — resuming the paused task automatically

Alternative Solutions

Currently there is no viable workaround. The user must be physically present at their Mac to approve dialogs. If they miss the 60-second window, the task silently fails and computer-use is blocked for the session until they return.

Priority

Critical - Blocking my work

Feature Category

Other

Use Case Example

User is on a long-haul flight with Cowork running autonomously on their Mac at home. Cowork needs computer-use access to open a new application it hasn't accessed before.

Currently: request_access triggers a dialog on the Mac screen. The 60-second timeout expires. Task silently fails. Computer-use is blocked for the rest of the session. User lands and finds incomplete work with no indication of what went wrong.

With this feature: User gets a push notification on their phone mid-flight. Dispatch shows an "Approve / Deny" message. User taps Approve. The dialog on Mac is dismissed. Task continues autonomously.

Additional Context

This affects Cowork + Dispatch users specifically. The two sub-issues are tightly linked — forwarding dialogs to Dispatch is only useful if Dispatch delivers push notifications to wake the user's phone. Both need to be implemented together to be effective.

Scope: Cowork macOS app + Dispatch + Claude iOS/Android app