Apply suggestions from code review

Co-authored-by: Tammy Baylis <[email protected]>

Author: xrmx

CHANGELOG.md

@@ -32,7 +32,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
   ([#3666](https://github.com/open-telemetry/opentelemetry-python-contrib/pull/3666))
 - `opentelemetry-sdk-extension-aws` Add AWS X-Ray Remote Sampler with initial Rules Poller implementation
   ([#3366](https://github.com/open-telemetry/opentelemetry-python-contrib/pull/3366))
-- `opentelemetry-instrumentation`: teach opentelemetry-instrument about gevent monkeypatching
+- `opentelemetry-instrumentation`: add support for  `OTEL_PYTHON_AUTO_INSTRUMENTATION_EXPERIMENTAL_GEVENT_PATCH` to inform opentelemetry-instrument about gevent monkeypatching
   ([#3699](https://github.com/open-telemetry/opentelemetry-python-contrib/pull/3699))
 
 ## Version 1.36.0/0.57b0 (2025-07-29)

opentelemetry-instrumentation/src/opentelemetry/instrumentation/auto_instrumentation/__init__.py

@@ -150,8 +150,8 @@ def initialize(*, swallow_exceptions: bool = True) -> None:
 
                 getattr(monkey, gevent_patch)()
             except ImportError:
-                _logger.error(
-                    "Requested to monkey patch with gevent but gevent is not available"
+                _logger.exception(
+                    "Failed to monkey patch with gevent because gevent is not available"
                 )
                 if not swallow_exceptions:
                     raise