[FEATURE] VSCode extension: actionable permission prompts directly in notifications (no tab switch required)

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 is running in one tab and pauses to ask for permission (e.g., "Allow shell command?"), it sends a VSCode notification. Clicking that notification switches you to the tab where the prompt is waiting, and only then can you click Allow or Deny.

Current flow:

1. Claude in Tab 1 hits a permission prompt → pauses and waits
2. You are working in Tab 2
3. VSCode notification fires: "Claude needs permission"
4. You click the notification → VSCode switches focus to Tab 1
5. You click Allow/Deny in the chat
6. You manually navigate back to Tab 2 to resume your work

The friction:

• Every permission prompt requires a full context switch: leave current tab → grant permission → navigate back
• In multi-tab workflows this can happen many times in a session, breaking flow repeatedly
• The notification itself has all the information needed to act — it just does not expose the action

Proposed Solution

Embed the permission action buttons directly in the VSCode notification so the user can approve or deny without leaving their current tab.

Proposed flow:

1. Claude in Tab 1 hits a permission prompt → pauses and waits
2. You are working in Tab 2
3. VSCode notification fires with inline buttons: "Allow" and "Deny" (and optionally "Allow Always")
4. You click Allow directly in the notification
5. Claude in Tab 1 resumes — you never left Tab 2

VSCode already supports this natively via vscode.window.showInformationMessage(message, ...items) which renders action buttons directly on the notification toast. This is a standard VSCode notification pattern used by many extensions (e.g., git push confirmation, test run prompts).

Alternative Solutions

The current behavior (notification → tab switch → click) is the fallback and should remain for cases where the user prefers to review the full context before deciding. The inline notification buttons would be an additive improvement on top of the existing behavior.

Priority

Medium - Improves my workflow

Feature Category

IDE integration (VSCode extension)

Use Case Example

1. I have Tab 1 running a refactor task and Tab 2 open for writing tests
2. Tab 1 reaches a shell command and Claude pauses: "Allow shell command: git push origin main?"
3. A VSCode notification appears with [Allow] and [Deny] buttons
4. I read the command in the notification, click [Allow] — all without leaving Tab 2
5. Claude in Tab 1 resumes; I never lost focus on my Tab 2 work

Additional Context

Related to #36089 (per-tab status indicators) — both address the multi-tab workflow experience in the VSCode extension.

The permission text shown in the notification should include enough context to make an informed decision (e.g., the specific command or file path being requested), not just a generic "permission needed" message.