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]

This is unrelated to the LoggingHandler

[avinab-neogy]

Sorry about that, I misread the issue scope. Having re-read #4738, the warning removal was out of scope, restored it. The PR now only documents the LoggingHandler move.

[xrmx]

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

[xrmx]

Are these really needed? Would be nice to test the examples

[avinab-neogy]

Tested this end to end with the collector, all 6 log records came through fine. I have added the explicit propagate=True based on this from #4738:

only the root logger is instrumented, so seen loggers must have propagate set to True

if you are loading logging settings with logging/.config.dictConfig, you must save the root loggers before applying dictConfig

Also tested locally that dictConfig with a root section does wipe the OTel handler completely. The explicit assignment is hence there as a reminder for users who might use dictConfig. Also happy to just keep it as a comment if you prefer.