Recent changes broke the Sentry AWS Lambda integration

Hello!

I am the maintainer of the [sentry-sdk](https://pypi.org/project/sentry-sdk/) for python. We have an integration with AWS Lambda that allows users to capture unhandled errors during AWS Lambda init or invocation.

There was a change recently: https://github.com/aws/aws-lambda-python-runtime-interface-client/pull/163/files#diff-4513a869520b19ae4e30058106d7c3b5ddbb79216b5e9bd922d83389fb86c603R481-R483

This breaks our integration, because we monkey patch `post_init_error` and use `sys.exc_info()` to access the currently handled exception.

With this change linked above the call to `post_init_error` has moved outside the exception handling block, so we no longer have access to the currently handled exception.

Is there any chance, we can move the call to `post_init_error` again under the exception handling block?

I have also a PR for this: https://github.com/aws/aws-lambda-python-runtime-interface-client/pull/171