Implement complete InferenceProvider system with OpenRouter integration

## Features
- 🔧 InferenceProvider interface with pluggable architecture
- 🔑 OpenRouter API key and OAuth PKCE authentication providers
- 🛠️ Tool calling support with automatic agent loop execution
- 📱 Interactive test UI with model selection and chat interface
- 🎯 Provider-level filtering to tool-capable models only
- ⚛️ React context with proper state management for UI reactivity

## Components
- Core types and interfaces in src/types/inference.ts
- OpenRouter client with shared utilities for both auth methods
- Two separate providers (composition over inheritance):
  - OpenRouterApiProvider for API key authentication
  - OpenRouterOAuthProvider for OAuth PKCE flow
- React InferenceContext with useInference hook
- Interactive test UI with tool calling demonstration
- OAuth callback routing with proper namespacing

## Tool Calling
- 3 test tools: weather, calculator, time
- Automatic tool execution and agent loop
- Visual tool call display with arguments and results
- Error handling for malformed tool calls

## Bug Fixes
- Fixed model selection UI reactivity issue
- Fixed OAuth popup race condition causing "cancelled" errors
- Proper cleanup of event listeners and intervals

## Documentation
- Comprehensive interface design document
- Implementation strategy and key design decisions
- Testing approach and security considerations

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

index.html

@@ -0,0 +1,13 @@
+<!doctype html>
+<html lang="en">
+  <head>
+    <meta charset="UTF-8" />
+    <link rel="icon" type="image/svg+xml" href="/vite.svg" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>Example Remote MCP Client</title>
+  </head>
+  <body>
+    <div id="root"></div>
+    <script type="module" src="/src/main.tsx"></script>
+  </body>
+</html>