Resolve "Remove proxy methods from Editor Lite's core"

What does this MR do?

This is a refactoring of Editor Lite core to get rid of the methods that just proxy to the methods of the same name from global editor to the editor's instance.

In !40257 (merged) we reviewed the architecture of the editor and changed it to allow multiple instances on one single global editor (with shared options and settings to begin with). This MR is the continuation of that work to move the API interactions further down to instance level instead of the global editor's level.

NB: There's no visible change in functionality, hence no changelog entry has been provided.

Screenshots

No visual changes

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

References #241025 (closed)