fix(llmobs): respect configured writer timeout in _send_payload

[jeong-hasang]

Description

BaseLLMObsWriter._send_payload opens its connection with get_connection(self._intake), passing no timeout argument.
As a result, it ignores the writer's own self._timeout and falls back to get_connection's DEFAULT_TIMEOUT of 2s.

On a high-latency connection to the agent/intake, the 2s socket timeout is exceeded at the tail. All retries hit the same 2s ceiling, so the batch is dropped (failed to send N LLMObs span events).

No env var works around this. _DD_LLMOBS_WRITER_TIMEOUT only sets self._timeout, which this path ignored.
DD_TRACE_AGENT_TIMEOUT_SECONDS is not consulted by the LLMObs writer.
In production, the only effective mitigation was monkeypatching get_connection to raise its default timeout — after which the timeouts disappeared, confirming the 2s default was the cause.

The fix passes timeout=self._timeout, restoring the 5s default that #9438 intended for the writer.

     def _send_payload(self, payload: bytes, num_events: int):
-        conn = get_connection(self._intake)
+        conn = get_connection(self._intake, timeout=self._timeout)

Testing

• Added regression test tests/llmobs/test_llmobs_span_agentless_writer.py::test_send_payload_uses_configured_timeout, which mocks get_connection and asserts _send_payload opens the connection with the writer's configured timeout (not DEFAULT_TIMEOUT).
• Ran the llmobs suite locally; the new test passes and no related tests regress.

Risks

Low. One-line change in a background flush thread — it does not block the request path. Behavior change: the effective LLMObs socket timeout goes from 2s to 5s (the intended _DD_LLMOBS_WRITER_TIMEOUT default). No public API change.

Additional Notes

Reproduced on 4.10.3; the bug is unchanged on main. Sibling timeout work for reference: #9438 (writer default 2s→5s)