The proxy auth path calls phase_span() and seed_request_identity() in
litellm/integrations/otel/runtime.py on every request, each doing a
try/except lazy import of litellm.integrations.otel.logger. When the
OpenTelemetry SDK is not installed (the default), that import raises, and
CPython never caches a failed import, so every request re-scanned sys.path
and contended on the import lock. At 750 concurrent users this cost about
12% throughput versus v1.85.0.
Resolve the hooks once and cache the outcome, absence included, with
functools.cache, so the import is attempted a single time instead of per
request. Throughput returns to the v1.85.0 baseline.
