Issue with the Re-login after sometime

## Problem

## Steps to reproduce the issue

## Expected behavior

1.It should either allow me to logout
2.It should have allowed me to re-authenticate

## System details (run `AWS: About` and/or `Amazon Q: About`)

## Error Logs
2025-12-08 14:49:55.459 [info] telemetry: sent batch (size=13)
2025-12-08 14:50:45.730 [error] amazon Q reauthenticate called on a non-existant connection
2025-12-08 14:50:45.730 [error] webviewId="aws.amazonq.AmazonCommonAuth": Error: Webview error
-> Error: Webview backend command failed: "reauthenticateConnection()"
-> Error: Cannot reauthenticate non-existant connection.
2025-12-08 14:52:54.253 [error] webviewId="aws.amazonq.AmazonCommonAuth": Error: Webview error
-> Error: Webview backend command failed: "signout()"
-> Error: Cannot signout non-SSO connection, type is: undefined
2025-12-08 14:52:55.744 [error] amazon Q reauthenticate called on a non-existant connection
2025-12-08 14:52:55.745 [error] webviewId="aws.amazonq.AmazonCommonAuth": Error: Webview error
-> Error: Webview backend command failed: "reauthenticateConnection()"
-> Error: Cannot reauthenticate non-existant connection.

- OS: Windows
- Visual Studio Code version: 1.106.3
- AWS Toolkit version:
- Amazon Q version:

Start by reproducing the Windows scenario described: close and reopen VS Code after the session expires, then try reauthenticate and signout. Trace the `reauthenticateConnection()` and `signout()` webview commands from the reported errors and inspect how the connection is restored. Done means both actions work instead of reporting a nonexistent or undefined connection.

Written by the indexing model from the issue text.