[CLEANUP] Improve code style of RelationHandler class

* add missing class properties, that are used in the code
* fix invalid PHPDoc variable types
* remove unused variables
* fix or remove invalid return values
* fix invalid variable types
* make sure unused variables are initialized

Resolves: #53718
Releases: 6.2
Change-Id: I90c1b73d0a4a7bb4666679e772805460786c805d
Reviewed-on: https://review.typo3.org/25479
Reviewed-by: Markus Klein
Tested-by: Markus Klein
Reviewed-by: Wouter Wolters
Reviewed-by: Stefan Neufeind
Tested-by: Stefan Neufeind