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/tasks.md

@@ -0,0 +1,29 @@
+## 1. Shared Models
+
+- [ ] 1.1 Create ChatRequest.cs in ChatAgent.Shared/Models with a Messages list property
+
+## 2. API Backend
+
+- [ ] 2.1 Add appsettings.json to ChatAgent.Api with ResponsesApi:BaseUrl and ResponsesApi:Model
+- [ ] 2.2 Register an HttpClient for the Responses API proxy in Api Program.cs
+- [ ] 2.3 Create ChatController with POST /api/chat that proxies to the Responses API with streaming
+- [ ] 2.4 Parse Responses API SSE stream, extract response.output_text.delta events, re-emit as simplified SSE to client
+
+## 3. Client Streaming
+
+- [ ] 3.1 Add a streaming SendChatAsync method to ChatApiClient that uses SetBrowserResponseStreamingEnabled and HttpCompletionOption.ResponseHeadersRead
+- [ ] 3.2 Parse the simplified SSE stream line-by-line, yielding text deltas
+
+## 4. Chat Page Updates
+
+- [ ] 4.1 Replace hardcoded response in Chat.razor with a call to ChatApiClient.SendChatAsync
+- [ ] 4.2 Append tokens to the assistant message incrementally with StateHasChanged after each delta
+- [ ] 4.3 Add a thinking indicator shown until the first token arrives
+- [ ] 4.4 Disable input field and send button while streaming is in progress
+- [ ] 4.5 Handle errors — display error message if API call fails
+- [ ] 4.6 Auto-scroll during streaming (not just at the end)
+
+## 5. Verify
+
+- [ ] 5.1 Run dotnet build to confirm no errors
+- [ ] 5.2 Manually verify: send a message, see streaming response from Claude