Refactor API structure: move chat functionality to v1 router, implement dependency injection for OpenAI client, and set up application state management

core/llm.py

@@ -0,0 +1,9 @@
+from openai import OpenAI
+
+
+def create_client(api_key: str) -> OpenAI:
+    """Factory for an OpenAI-compatible client pointed at DeepSeek."""
+    return OpenAI(
+        api_key=api_key,
+        base_url="https://api.deepseek.com",
+    )