Add instrumentation example to logging

[andremm]

Description

There's no instrumentation examples inside logging. This PR adds one example.

Type of change

Please delete options that are not relevant.

• Bug fix (non-breaking change which fixes an issue)

How Has This Been Tested?

1. Clone contrib repo: git clone https://github.com/open-telemetry/opentelemetry-python-contrib
2. Clone OTel Python repo: git clone https://github.com/open-telemetry/opentelemetry-python
3. Access the contrib repo: cd opentelemetry-python-contrib
4. Create a virtual env: python3 -m venv otelvenv
5. Activate the virtual env: source otelvenv/bin/activate
6. Install common dependencies:

pip install opentelemetry-distro/ opentelemetry-instrumentation/ \
 ../opentelemetry-python/opentelemetry-semantic-conventions/ \
 ../opentelemetry-python/opentelemetry-api/ \
 ../opentelemetry-python/opentelemetry-sdk/ \
 ../opentelemetry-python/opentelemetry-proto/ \
 ../opentelemetry-python/exporter/opentelemetry-exporter-otlp-proto-common

7. Install logging specific requirements:

pip install -r instrumentation/opentelemetry-instrumentation-logging/test-requirements.txt

8. Copy the instrumentation examples inside the instrumentation main __init__.py file into different Python files and try to run them.

Does This PR Require a Core Repo Change?

• Yes. - Link to PR:
• No.

Checklist:

See contributing.md for styleguide, changelog guidelines, and more.

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