flaky test test_send_remote_failover_sync_non_transport_exception_error

**Describe the bug**:

Cannot reproduce reliably still may be useful to fix:

```
=================================== FAILURES ===================================
_________ test_send_remote_failover_sync_non_transport_exception_error _________

should_try =
http_send =
caplog = <_pytest.logging.LogCaptureFixture object at 0x7f943c8a5c90>

@mock.patch("elasticapm.transport.http.Transport.send")
@mock.patch("elasticapm.transport.base.TransportState.should_try")
def test_send_remote_failover_sync_non_transport_exception_error(should_try, http_send, caplog):
should_try.return_value = True

client = Client(
server_url="http://example.com",
service_name="app_name",
secret_token="secret",
transport_class="elasticapm.transport.http.Transport",
metrics_interval="0ms",
metrics_sets=[],
)
# test error
http_send.side_effect = ValueError("oopsie")
with caplog.at_level("ERROR", "elasticapm.transport"):
client.capture_message("foo", handled=False)
client._transport.flush()
assert client._transport.state.did_fail()
assert_any_record_contains(caplog.records, "oopsie", "elasticapm.transport")

# test recovery
http_send.side_effect = None
client.capture_message("foo", handled=False)
client.close()
> assert not client._transport.state.did_fail()
E assert not True
E + where True = >()
E + where > = .did_fail
E + where = .state
E + where = ._transport

tests/client/client_tests.py:288: AssertionError
----------------------------- Captured stderr call -----------------------------
{"@timestamp":"2024-03-06T16:09:14.917Z","log.level":"error","message":"Failed to submit message: 'oopsie'","ecs":{"version":"1.6.0"},"log":{"logger":"elasticapm.transport","origin":{"file":{"line":318,"name":"base.py"},"function":"handle_transport_fail"},"original":"Failed to submit message: 'oopsie'"},"process":{"name":"MainProcess","pid":905083,"thread":{"id":140274711856704,"name":"eapm event processor thread"}},"service":{"name":"app_name"}}
{"@timestamp":"2024-03-06T16:09:14.917Z","log.level":"error","message":"Failed to submit message: 'oopsie'","ecs":{"version":"1.6.0"},"log":{"logger":"elasticapm.transport","origin":{"file":{"line":318,"name":"base.py"},"function":"handle_transport_fail"},"original":"Failed to submit message: 'oopsie'"},"process":{"name":"MainProcess","pid":905083,"thread":{"id":140274711856704,"name":"eapm event processor thread"}},"service":{"name":"app_name"}}
------------------------------ Captured log call -------------------------------
{"@timestamp":"2024-03-06T16:09:14.917Z","log.level":"error","message":"Failed to submit message: 'oopsie'","ecs":{"version":"1.6.0"},"log":{"logger":"elasticapm.transport","origin":{"file":{"line":318,"name":"base.py"},"function":"handle_transport_fail"},"original":"Failed to submit message: 'oopsie'"},"process":{"name":"MainProcess","pid":905083,"thread":{"id":140274711856704,"name":"eapm event processor thread"}},"service":{"name":"app_name"}}
=============================== warnings summary ===============================
```

**To Reproduce**

1. pytest

**Environment (please complete the following information)**
- OS: [e.g. Linux] Linux
- Python version: 3.10.12
- Framework and version [e.g. Django 2.1]:
- APM Server version:
- Agent version:

**Additional context**

None