[C++][FlightRPC] DoAction cannot be fully streaming

[lidavidm]

As noted by Kou, existing applications/tests may assume that DoAction is not actually a streaming call.

This might break wheel-macos-big-sur-*. For example: https://github.com/ursacomputing/crossbow/actions/runs/3815472986/jobs/6490471956#step:11:435

=================================== FAILURES ===================================
_________________________ test_none_action_side_effect _________________________

    def test_none_action_side_effect():
        """Ensure that actions are executed even when we don't consume iterator.
    
        See https://issues.apache.org/jira/browse/ARROW-14255
        """
    
        with ActionNoneFlightServer() as server, \
                FlightClient(('localhost', server.port)) as client:
            client.do_action(flight.Action("append", b""))
            r = client.do_action(flight.Action("get_value", b""))
>           assert json.loads(next(r).body.to_pybytes()) == [True]
E           assert [] == [True]
E             Right contains one more item: True
E             Full diff:
E             - [True]
E             + []

test-arm64-env/lib/python3.10/site-packages/pyarrow/tests/test_flight.py:2132: AssertionError
----------------------------- Captured stderr call -----------------------------
/Users/voltrondata/github-actions-runner/_work/crossbow/crossbow/arrow/cpp/src/arrow/status.cc:137: DoAction result was not fully consumed: Cancelled: Flight cancelled call, with message: CANCELLED. Detail: Cancelled

Originally posted by @kou in #15118 (comment)