feat(sdk-logs)!: Removed deprecated LoggerProvider#addLogRecordProcessor()

[svetlanabrennan]

Which problem is this PR solving?

Removed deprecated LoggerProvider#addLogRecordProcessor() in favor os the constructor option. See linked issue for more details.

Fixes #5738
Related PR: open-telemetry/opentelemetry-js-contrib#2895

Short description of the changes

• Removed LoggerProvider#addLogRecordProcessor()
• Updated exporters readme mention of adding this logger provider
• Updated test
• Removed addLogRecordProcessor from the contrib repos

Type of change

Please delete options that are not relevant.

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

How Has This Been Tested?

Updated test

Checklist:

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

TODOs

• Remove addLogRecordProcessor from contrib repo

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.01%. Comparing base (e18a6c8) to head (75d9869).
Report is 2 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #5764   +/-   ##
=======================================
  Coverage   95.01%   95.01%           
=======================================
  Files         303      303           
  Lines        7957     7950    -7     
  Branches     1609     1608    -1     
=======================================
- Hits         7560     7554    -6     
+ Misses        397      396    -1     

Files with missing lines	Coverage Δ
...perimental/packages/sdk-logs/src/LoggerProvider.ts	100.00% <ø> (+2.22%)	⬆️

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[hectorhdzg]

LGTM

[pichlermarc]

Looks good, thank you 🙂