refactor(fc2c-i): single shared async engine with lifecycle dispose

tests/test_extensions_session.py

@@ -0,0 +1,31 @@
+"""Unit: the shared engine is a memoized singleton; dispose resets it.
+
+create_async_engine does NOT open a connection, so identity checks need no
+DB and run in CI (not integration-marked).
+"""
+
+import pytest
+
+from backend.app import extensions
+
+
+@pytest.mark.asyncio
+async def test_get_engine_is_singleton():
+    a = extensions.get_engine()
+    b = extensions.get_engine()
+    assert a is b
+    await extensions.dispose_engine()
+
+
+@pytest.mark.asyncio
+async def test_dispose_engine_allows_fresh_engine():
+    first = extensions.get_engine()
+    await extensions.dispose_engine()
+    second = extensions.get_engine()
+    assert first is not second
+    await extensions.dispose_engine()
+
+
+def test_get_session_returns_async_context_manager():
+    cm = extensions.get_session()
+    assert hasattr(cm, "__aenter__") and hasattr(cm, "__aexit__")