Amazon Q requiring authorization every time after logging in and wiping chat content pre authorization

## Problem
After authenticating with Q Developer on the extension the chat opens. If you try to write something to the chat it prompts you every time to re-authorize Q (even though you just logged in) and deletes whatever you wrote in the chat.

## Steps to reproduce the issue
1. Click Q on the left side toolbar
2. Authenticate via the browser
3. Try to write something to the chat
4. Observe the authentication prompt showing up again

## Expected behavior
After logging in, you should be prompted to authorize Q immediately and if that's not possible at least the chat content that you wrote before authorizing Q should not be cleared afterwards.

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

- OS: macOS 15.3.1
- Visual Studio Code version: 1.105.1 (Universal)
- AWS Toolkit version: N/A
- Amazon Q version: 1.102.0

Start at the Amazon Q chat entry point opened from the left toolbar and reproduce the browser authentication flow on the stated macOS and VS Code versions. Trace why authorization is requested again when the user first types and verify that successful authorization no longer repeats the prompt or clears the pre-authorization chat content.

Written by the indexing model from the issue text.