[TASK] Simplify filesystem usage in PackageArtifactBuilder

Only create one filesystem object,
instead of always creating new ones where needed.

Resolves: #101870
Releases: main, 12.4, 11.5
Change-Id: I56a47f412fded7585425098f18f1d7090baf09d1
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/80923


Tested-by: core-ci <typo3@b13.com>
Reviewed-by: Benjamin Franzke <ben@bnf.dev>
Tested-by: Benjamin Franzke <ben@bnf.dev>