In `@backend/app/database/core.py`:
- Around line 46-57: Remove the redundant explicit close in the async session
context manager: when using the async with async_session_maker() as session
block you should not call await session.close() in the finally; delete that call
so the context manager handles cleanup. Also replace logger.error(...) with
logger.exception(...) in the except block to include the traceback, while
preserving await session.rollback() and re-raising the exception; reference
async_session_maker, session, logger.error -> logger.exception, session.rollback
to locate the changes.

In `@tests/test_db_pool.py`:
- Around line 7-9: The test currently patches app.core.config.settings at module
scope but imports engine and get_db after the patch context, which is fragile
because engine is created at import time and module caching prevents
reinitialization; update tests/test_db_pool.py to apply the patch while
importing/reloading the database module so engine is created with the mocked
configuration—use a pytest fixture that applies patch.dict or patch to set
DATABASE_URL (or patch app.core.config.settings), then
importlib.reload(app.database.core) inside that fixture and yield db_core.engine
and db_core.get_db (or move the import of engine/get_db inside the with
patch(...) block) so engine initialization sees the mocked value.
- Around line 44-45: The async context manager mock is incomplete: instead of
assigning __aexit__.return_value = None make both __aenter__ and __aexit__
awaitable (e.g., replace the current assignments on mock_session with AsyncMock
usage: set mock_session.__aenter__ = AsyncMock(return_value=mock_session) and
mock_session.__aexit__ = AsyncMock(return_value=None)), and apply the same
change to the other async context-manager mock later in the file so both
enter/exit are proper awaitables.