Fix #2689 LoggingHandler to handle exc_info=False

[gen-xu]

Description

Please include a summary of the change and which issue is fixed. Please also include relevant motivation and context. List any dependencies that are required for this change.

Fixes #2689

Type of change

Please delete options that are not relevant.

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

How Has This Been Tested?

Please describe the tests that you ran to verify your changes. Provide instructions so we can reproduce. Please also list any relevant details for your test configuration

• opentelemetry-sdk/tests/logs/test_handler.py::test_log_exc_info_false

Does This PR Require a Contrib Repo Change?

Answer the following question based on these examples of changes that would require a Contrib Repo Change:

• The OTel specification has changed which prompted this PR to update the method interfaces of opentelemetry-api/ or opentelemetry-sdk/

• The method interfaces of test/util have changed

• Scripts in scripts/ that were copied over to the Contrib repo have changed

• Configuration files that were copied over to the Contrib repo have changed (when consistency between repositories is applicable) such as in

  • pyproject.toml
  • isort.cfg
  • .flake8

• When a new .github/CODEOWNER is added

• Major changes to project information, such as in:

  • README.md
  • CONTRIBUTING.md

• Yes. - Link to PR:

• No.

Checklist:

• Followed the style guidelines of this project
• Changelogs have been updated
• Unit tests have been added
• Documentation has been updated

[linux-foundation-easycla]

The committers listed above are authorized under a signed CLA.

• ✅ login: gen-xu / name: Gen Xu (6b41a64)