[BUGFIX] Tests: Refactor log writer tests in ext:core

Test files and class naming is adapted to subject class names in
ext:core Log/Writer and the DatabaseWriterTests are rewritten to
not depend on initialized database connection anymore.

Change-Id: Ifff4e5a064018bb5b0db3bf9eeb1b9232adfb262
Resolves: #56921
Related: #51436
Releases: 6.2
Reviewed-on: https://review.typo3.org/28396
Reviewed-by: Wouter Wolters
Tested-by: Wouter Wolters
Reviewed-by: Anja Leichsenring
Tested-by: Anja Leichsenring