feat(backend): setup FastAPI + SQLite + config

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/app/database.py

@@ -0,0 +1,13 @@
+from sqlmodel import SQLModel, create_engine, Session
+from app.config import DATABASE_URL
+
+engine = create_engine(DATABASE_URL, connect_args={"check_same_thread": False})
+
+
+def get_session():
+    with Session(engine) as session:
+        yield session
+
+
+def create_db_and_tables():
+    SQLModel.metadata.create_all(engine)