[FEATURE] Right-click context menu to rename sessions in VS Code extension

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

Renaming a session currently requires hovering over it to reveal a hidden icon, which is unintuitive and doesn't match standard VS Code / Windows UX patterns. The rename action also doesn't auto-refresh the session title after saving.
Proposed Solution:

Proposed Solution

Add "Rename" to the right-click context menu on session entries, consistent with how VS Code and Windows handle renaming (files, tabs, etc.)
Auto-refresh the session title immediately after renaming without requiring a manual reload.

Why:
Right-click → Rename is the universal expectation in any Windows/VS Code environment. The current hover-reveal pattern is a discoverability problem — most users won't find it.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

API and model interactions

Use Case Example

Scenario: A developer juggling multiple features at once
You're working on a web application and have 3 Claude sessions open in VS Code:

One session fixing a login authentication bug
One session writing unit tests for the payment module
One session brainstorming the UI redesign for the dashboard

Step 1: Each session title auto-generates from the first words typed — you end up with tabs like "The login button stops w...", "Can you help me write t...", "I want to redesign the...". All meaningless at a glance.
Step 2: You want to rename them to Auth Bug, Payment Tests, Dashboard UI. You hover over a session, find the hidden icon, click, type — but the title doesn't update until you reload. You repeat this for each session.
Step 3: 30 minutes later you've lost track of which session is which again and you're clicking through tabs to reorient yourself.
The ask: Right-click the session → "Rename" → type new name → title updates instantly. The same way you'd rename a file in VS Code's Explorer, a browser tab group, or any standard Windows interface.

Additional Context

_No response_