Please remove the cleared conversation history

"Please remove the cleared conversation history, because in this way we lose our work. It is difficult for us to understand the AI again, which is not what we want."

Start by tracing the Amazon Q conversation-clearing flow in the VS Code extension and determine what history is removed and whether work can be retained. Clarify the intended behavior with maintainers; done means the expected conversation history is preserved after clearing without losing user work.

Written by the indexing model from the issue text.