Amazon Q: too easy to accidentally click the suggested follow questions

## Problem

Myself (`@bwith` at amazon) and my coworker constantly click the Suggested follow up questions by mistake trying to access the chat box. Then we have to wait until it fully responds to the accidental click.

## Expected behavior

Ideas:
- Move suggested follow up questions
- Remove suggested follow up questions
- Make it a two click action

The issue names no files, tests, or entry points. Start by locating the Amazon Q Suggested follow up questions UI in the VS Code extension and compare its click target with the chat box. Decide which interaction change is intended, then verify that accidental activation is prevented while intentional follow-up use still works.

Written by the indexing model from the issue text.