fix(internal): writer recreate maintain extra headers (#9424)

internal: this fixes an issue where a writer recreate call would make it
drop extra headers passed to the ``__init__``.

## Checklist

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- [x] Testing strategy is described if automated tests are not included
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## Reviewer Checklist

- [x] Title is accurate
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ddtrace/internal/writer/writer.py

@@ -539,6 +539,7 @@ def recreate(self):
             dogstatsd=self.dogstatsd,
             sync_mode=self._sync_mode,
             api_version=self._api_version,
+            headers=self._headers,
         )
 
     @property

tests/tracer/test_writer.py

@@ -706,6 +706,16 @@ def test_writer_recreate_api_version(init_api_version, api_version, endpoint, en
     assert isinstance(writer._encoder, encoder_cls)
 
 
+def test_writer_recreate_keeps_headers():
+    writer = AgentWriter("http://dne:1234", headers={"Datadog-Client-Computed-Stats": "yes"})
+    assert "Datadog-Client-Computed-Stats" in writer._headers
+    assert writer._headers["Datadog-Client-Computed-Stats"] == "yes"
+
+    writer = writer.recreate()
+    assert "Datadog-Client-Computed-Stats" in writer._headers
+    assert writer._headers["Datadog-Client-Computed-Stats"] == "yes"
+
+
 @pytest.mark.parametrize(
     "sys_platform, api_version, ddtrace_api_version, priority_sampling, raises_error, expected",
     [