I think I prefer this version:

    class Session:
        def __init__(self):
            self._connection = db.connect(...)

        def __enter__(self):
            self._connection.__enter__(self)
            return self

        def __exit__(self, *args):
            return self._connection.__exit__(self)

        def login(self, name, password):
            self._connection.query(...)

    with Session() as session:
        ...

It might need a bit more knowledge about context managers [1], but it feels less magic and more explicit to me – i.e. more pythonic :). But it also contains the assumption that db.connection already returns the connection. If that is not true, a bit more housekeeping is needed:

    class Session:
        def __init__(self):
            self._connection_context = db.connect(...)

        def __enter__(self):
            self._connection = self._connection_context.__enter__(self)
            return self

        def __exit__(self, *args):
            return self._connection_context.__exit__(self)

        def login(self, name, password):
            self._connection.query(...)

[1] https://docs.python.org/3/library/stdtypes.html#typecontextm...