Copilot Chat: Draft in new chat is lost after switching conversations

### Problem summary
In a **new Copilot Chat conversation**, if I type a draft in the chat textarea (without sending), switch to another existing conversation, and then return to the new conversation, the typed draft is lost.

### Contrast with current behavior in ongoing sessions
In an **ongoing/existing conversation**, switching away and returning preserves the unsent draft in the textarea.

### Expected behavior
A draft typed in a **new conversation** should persist when switching to another conversation and coming back, matching the behavior of ongoing conversations.

### Steps to reproduce
1. Open Copilot Chat in VS Code.
2. Start a **new chat**.
3. Type text in the input textarea, but do **not** send it.
4. Switch to a different, previously existing conversation.
5. Return to the new chat started in step 2.

### Current behavior
The draft typed in step 3 is cleared or lost.

### Expected result
The draft should still be present after returning to the new chat.

### Environment
- OS: Windows
- Product: Visual Studio Code
- Area: GitHub Copilot Chat