Is your suggestion for improvement related to a problem? Please describe.
Some logic in org.jabref.logic.cleanup is placed in the wrong layer or mixes responsibilities:

• Formatter is a base class for string formatters but lives in the cleanup package.
• FieldFormatterCleanups handles both parsing/serialization and cleanup execution

Describe the solution you'd like

• Move Formatter to org.jabref.logic.formatter.
• Refactor and rename FieldFormatterCleanups and extract its parsing logic to a small helper like FieldFormatterCleanupParser.
• Keep public behavior unchanged.

Additional context
This is a small, non-functional refactor touching mainly:

• Formatter.java (moved)
• FieldFormatterCleanups.java (renamed + internal refactor)
  with only minor import updates in related logic and test