Code review noted the previous test reimplemented the proxy's
try/except/finally around post_call_success_hook, so it would not catch a
regression that re-introduced the duplicate-log bug in the production code
path. Extract the gating logic into
`ProxyBaseLLMRequestProcessing._flush_deferred_async_logging` so tests
exercise the production helper directly.
The proxy finally block becomes a single call to the helper. Tests now
invoke the helper itself and additionally assert (via inspect.getsource)
that base_process_llm_request continues to delegate to the helper rather
than inlining the gate.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
