## Context

Chat.razor currently constructs a `ChatRequest` with only the latest user message (line 161-164). The backend and Responses API already support multi-message input — no server changes needed. This is purely a client-side change.

## Goals / Non-Goals

**Goals:**
- Send full conversation history with each request for multi-turn context
- Add a "New Chat" button to reset the session

**Non-Goals:**
- Persistent conversation storage (explicitly deferred)
- Multiple conversation tabs/sidebar
- Token limit management or history truncation (small conversations for now)

## Decisions

### Decision 1: Send full _messages list minus the empty placeholder

When building the `ChatRequest`, include all messages from `_messages` except the last one (which is the empty assistant placeholder waiting for streaming). This gives the AI the full conversation context.

### Decision 2: New Chat button in the AppBar

Place a "New Chat" icon button in the `MudAppBar` (in MainLayout.razor or Chat.razor). Clicking it clears `_messages` and resets to the empty state. Disabled during streaming.

Alternative considered: putting it in the input area. Rejected — the AppBar is more natural and matches ChatGPT/Gemini placement.

## Risks / Trade-offs

- [No token limit management] → For long conversations, the full history could exceed the model's context window. Acceptable for now; truncation can be added later.