[FEATURE] VS Code Extension: Support queued message sending instead of interrupting current task

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

When Claude Code VS Code extension is running a task, if I send a new message, it interrupts the current task immediately. This is disruptive to my workflow — I often want to queue up the next instruction while waiting for the current task to finish, not stop it mid-execution.

Proposed Solution

Add a message queue feature to the VS Code extension. When Claude is busy running a task, any new message sent by the user should be held in a queue and automatically sent once the current task completes — instead of interrupting the running task.

The interface should show a visual indicator (e.g., "1 message queued") so the user knows their message has been received and will be processed next.

Optionally, the user could also cancel the queued message before it's sent.

Alternative Solutions

Currently, the only workaround is to wait for the task to finish before typing the next message. There is no built-in queuing mechanism.

Other AI coding tools (e.g., Cursor) offer a similar "queue" or "wait" behavior that prevents accidental task interruption.

Priority

High - Significant impact on productivity

Feature Category

Developer tools/SDK

Use Case Example

1. I ask Claude Code VS Code extension to refactor a large module — this takes ~30 seconds.
2. 2. While it's running, I think of the next step: "also update the tests."
3. 3. I type "also update the tests" and hit Enter.
4. 4. Current behavior: Claude stops the refactoring mid-way and starts working on the tests instead.
5. 5. Expected behavior: Claude finishes the refactoring first, then automatically processes "also update the tests" from the queue.

This would allow me to think ahead and queue instructions without disrupting Claude's current focus.

Additional Context

_No response_