feat: add basic chat interface with MudBlazor and propose responses API integration

Install MudBlazor 9.2.0, replace Bootstrap layout with MudLayout/MudAppBar,
create Chat.razor with message list, text input, auto-scroll, and hardcoded
responses. Add ChatMessage shared model. Remove template pages (Counter,
Weather), move health check to /health. Include OpenSpec change artifacts
for the upcoming wire-responses-api work.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

openspec/changes/wire-responses-api/proposal.md

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+## Why
+
+The chat UI currently returns hardcoded responses. A local OpenAI-compatible proxy is running at `localhost:8317` that exposes the Responses API (`POST /v1/responses`) backed by Anthropic Claude models. This change wires the chat to produce real AI responses via streaming, replacing the hardcoded stub.
+
+## What Changes
+
+- Add a chat endpoint to the API backend that proxies requests to the local Responses API
+- Stream tokens from the Responses API back to the WASM client as SSE
+- Update ChatApiClient with a streaming chat method
+- Replace the hardcoded response in Chat.razor with live streaming from the API
+- Add a "thinking" indicator while the assistant is responding
+- Disable input during streaming to prevent overlapping requests
+
+## Capabilities
+
+### New Capabilities
+- `chat-streaming`: Streaming AI responses from the Responses API proxy through the backend to the WASM client
+
+### Modified Capabilities
+- `chat-ui`: Replace hardcoded response with streaming AI response, add typing indicator, disable input during streaming
+
+## Impact
+
+- `src/ChatAgent.Api/ChatAgent.Api.csproj`: Add no new packages (uses built-in HttpClient)
+- `src/ChatAgent.Api/Controllers/ChatController.cs`: New controller proxying to Responses API
+- `src/ChatAgent.Api/Program.cs`: Register HttpClient for the proxy, add configuration
+- `src/ChatAgent.Api/appsettings.json`: New — configure Responses API base URL and model
+- `src/ChatAgent.Client/Services/ChatApiClient.cs`: Add streaming chat method
+- `src/ChatAgent.Client/Pages/Chat.razor`: Replace hardcoded response with streaming call
+- `src/ChatAgent.Shared/Models/`: New request/response DTOs for the chat endpoint