Move logs to core

What does this MR do?

Moves the logging related code from EE to Core. &2484 (closed)

Since these are mostly straight renames, the overhead of opening 5 MRs each moving a separate category of files, while keeping the codebase consistent and working at any point in time, along with multi-week review delays, made me think one MR is probably better and small enough in that specific case.

Related issues #198451 (closed) #198452 (closed) #198453 (closed) #198454 (closed) #198455 (closed)

Screenshots

Does this MR meet the acceptance criteria?

Conformity

• Changelog entry
• Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• Database guides
• Separation of EE specific content

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers
• Informed Infrastructure department of a default or new setting change, if applicable per definition of done

Security

If this MR contains changes to processing or storing of credentials or tokens, authorization and authentication methods and other items described in the security review guidelines:

• Label as security and @ mention @gitlab-com/gl-security/appsec
• The MR includes necessary changes to maintain consistency between UI, API, email, or other methods
• Security reports checked/validated by a reviewer from the AppSec team