Remove logs API proxy test's dependency on SDK

[aabmass]

Description

The change is pretty self explanatory. API test shouldn't generally depend on the SDK and it was completely unnecessary here.

The Logger.emit() function shouldn't actually return anything, based on the ABC https://github.com/open-telemetry/opentelemetry-python/blob/29c293fbb120ff8b760519a25e0530b5ab05af83/opentelemetry-api/src/opentelemetry/_logs/_internal/__init__.py#L100-L102

Type of change

Please delete options that are not relevant.

• [x] Chore (test fix)

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

• [x] Updated the test and it passes

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

• [x] No.

Checklist:

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