[exporter/logging] Remove logging exporter

[TylerHelmuth]

Description

It is September, which means we get to remove this deprecated component.

• The helm chart was updated to exclude the logging exporter already: https://github.com/open-telemetry/opentelemetry-helm-charts/blob/main/charts/opentelemetry-collector/UPGRADING.md#0840-to-0850.
• The Operator references have been updated: [chore] Remove references to the logging exporter opentelemetry-operator#3259.
• Opentelemetry.io site final references to update: [chore] Remove references to the logging exporter opentelemetry.io#5143

Link to tracking issue

Related to #7769

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.42%. Comparing base (296e789) to head (42001aa).
Report is 4 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #11037      +/-   ##
==========================================
- Coverage   91.42%   91.42%   -0.01%     
==========================================
  Files         424      422       -2     
  Lines       20187    20117      -70     
==========================================
- Hits        18455    18391      -64     
+ Misses       1348     1343       -5     
+ Partials      384      383       -1     

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[mx-psi]

There are a bunch of references on examples in language library repositories still that mention the logging exporter. This search has a lot of false positives, but it's a good start I think: https://github.com/search?q=org%3Aopen-telemetry+%22logging%3A%22+-repo%3Aopen-telemetry%2Fopentelemetry-collector+language%3AYAML+OR+language%3AMarkdown&type=code&p=1

We also have ~18% of survey respondents from the Collector survey raw data using the logging exporter so I think we need to do this very carefully.

At a minimum I feel like we need a migration page, and a very clear error message that tells you to use the debug exporter and links you to the migration page. Additionally, it would be great to have something like #7631 before we do this (not sure if it should be a hard requirement tho).

I am blocking this until we at least have no references to the logging exporter within examples in the OpenTelemetry org

[TylerHelmuth]

@mx-psi it has been another 4 weeks with an even louder warning and @codeboten has updated a majority of the loggingexporter references in language repos. I feel we should move forward with this removal.