docs: update logs example to use opentelemetry-instrumentation-logging

[avinab-neogy]

Description

Update the logs example documentation to reflect that LoggingHandler
has moved from the SDK to the contrib package.

Refs #4738

Changes made:

• Add Installation section with correct pip installs including opentelemetry-instrumentation-logging
• Add Run the Example section for better structure
• Add note that LoggingHandler has moved to opentelemetry-instrumentation-logging (deprecated in opentelemetry-sdk: deprecate logging handler #4919)
• Add propagate=True with explanation comment in example.py

Type of change

• This change requires a documentation update

How Has This Been Tested?

• Built docs locally with tox -e docs — build succeeded with no warnings
• Ran tox -e spellcheck — passed
• Verified rendered HTML output looks correct

Does This PR Require a Contrib Repo Change?

• 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: avinab-neogy / name: avinab-neogy (0ddf26c)

[xrmx]

I think your changes are not very relevant with #4738 but the changes regarding the LoggingHandler move are good

[hectorhdzg]

LGTM