feat(test): Add flush to async transport test

Add flush to async transport test matrix. Additionally, explicitly shut down the worker task upon flushing in the tests,
to avoid event loop errors.

GH-4601

Author: srothh

tests/test_transport.py

@@ -151,7 +151,7 @@ def test_transport_works(
 
 @pytest.mark.asyncio
 @pytest.mark.parametrize("debug", (True, False))
-@pytest.mark.parametrize("client_flush_method", ["close"])
+@pytest.mark.parametrize("client_flush_method", ["close", "flush"])
 @pytest.mark.parametrize("use_pickle", (True, False))
 @pytest.mark.parametrize("compression_level", (0, 9, None))
 @pytest.mark.parametrize("compression_algo", ("gzip", "br", "<invalid>", None))
@@ -203,6 +203,8 @@ async def test_transport_works_async(
 
     if client_flush_method == "close":
         await client.close(timeout=2.0)
+    if client_flush_method == "flush":
+        await client.flush(timeout=2.0)
 
     out, err = capsys.readouterr()
     assert not err and not out
@@ -222,8 +224,11 @@ async def test_transport_works_async(
     )
 
     assert capturing_server.captured[0].compressed == should_compress
-
+    # After flush, the worker task is still running, but the end of the test will shut down the event loop
+    # Therefore, we need to explicitly close the client to clean up the worker task
     assert any("Sending envelope" in record.msg for record in caplog.records) == debug
+    if client_flush_method == "flush":
+        await client.close(timeout=2.0)
 
 
 @pytest.mark.parametrize(