[FEATURE] [VSCODE] Allow fast account toggle and show current logged in email

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

At work we are testing different providers, one of them is Claude.

Since I already have a private subscription, I find myself constantly needing to logout and login in VS Code, which is inconvinient.

But, the worst problem is that unless we manually check "Account & Usage", there is nothing that shows which is the current logged in account which leads to either exposing my private projects to company usage or using my tokens for work. Both are bad.

Proposed Solution

1. Show always the logged in account at the top of the chat window in VSCODE
2. Allow to do fast account switch (2 accounts logged in at the time).

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

Other

Use Case Example

_No response_

Additional Context

_No response_