[ENH]: remove unused log service code

[nicolasgere]

Description of changes

Summarize the changes made by this PR.

• Improvements & Bug fixes
  • ...
• New functionality
  • ...

Test plan

How are these changes tested?

• Tests pass locally with pytest for python, yarn test for js, cargo test for rust

Documentation Changes

Are all docstrings for user-facing APIs updated if required? Do we need to make documentation changes in the docs repository?

[nicolasgere]

• [ENH]: remove unused log service code #1973 👈
• [ENH]: Use new log service #1971
• [ENH]: Add property test log service #1969
• main

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[github-actions]

Reviewer Checklist

Please leverage this checklist to ensure your code review is thorough before approving

Testing, Bugs, Errors, Logs, Documentation

• Can you think of any use case in which the code does not behave as intended? Have they been tested?
• Can you think of any inputs or external events that could break the code? Is user input validated and safe? Have they been tested?
• If appropriate, are there adequate property based tests?
• If appropriate, are there adequate unit tests?
• Should any logging, debugging, tracing information be added or removed?
• Are error messages user-friendly?
• Have all documentation changes needed been made?
• Have all non-obvious changes been commented?

System Compatibility

• Are there any potential impacts on other parts of the system or backward compatibility?
• Does this change intersect with any items on our roadmap, and if so, is there a plan for fitting them together?

Quality

• Is this code of a unexpectedly high quality (Readability, Modularity, Intuitiveness)