Amazon Q VS Code Extension Lacks OAuth Authentication Support over HTTP Transport

## Problem

The Amazon Q VS Code Extension does not support OAuth authentication when configuring an MCP using the **streamable-http** transport type.

This issue does not occur when using the Amazon Q CLI, following the steps in the [AWS Documentation](https://docs.aws.amazon.com/amazonq/latest/qdeveloper-ug/command-line-mcp-config-CLI.html).

## Steps to reproduce the issue

Steps to Reproduce

1. Set up an MCP with the HTTP transport type in the Amazon Q VS Code Extension.

2. Attempt to authenticate using OAuth.

3. Observe the resulting error.

I see the following SSE error: _**failed to connect: Non-200 status code (401)**_

## Expected behavior

The MCP should provide a URL for OAuth authentication, similar to the behavior observed when using the Amazon Q CLI.

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

- OS: macOS Sequoia 15.7.1
- Visual Studio Code version: 1.99.3
- Amazon Q version: 1.103.0

Start by tracing the Amazon Q VS Code Extension's MCP streamable-http connection and OAuth authentication flow, then compare it with the Amazon Q CLI behavior described in the AWS Documentation. Reproduce the 401 SSE error with an HTTP MCP and verify that the extension provides an OAuth authentication URL and completes authentication successfully.

Written by the indexing model from the issue text.