There's no mention of $logger in the said method, includes/filerepo/file/NSLocalFile.php#L322-L355 (in fact in the whole repo), so changing the property visibility will not fix the actual problem.

$logger is probably null at that stage because a subclass at NSLocalFileMoveBatch#L424 defines its constructor and does not call the parent one — which sets the property. I think this would be fixed if the extension's class call its parent constructor

Good point! I've tested this and can confirm the following change to extensions/NSFileRepo/includes/filerepo/file/NSLocalFile.php starting at line 429 works.
So to be clear, my original proposition of altering mediawiki's LocalFileMoveBatch class is *not* necessary, indeed.
Apologies for my misunderstanding of the correct solution direction.

class NSLocalFileMoveBatch extends LocalFileMoveBatch {
	/**
	 * @param LocalFile $file
	 * @param Title $target
	 */
	public function __construct( LocalFile $file, Title $target ) {
		parent::__construct( $file, $target );
		$this->oldRel = $this->oldHash . NSLocalFile::getFileNameStripped( $this->oldName );
		$this->newRel = $this->newHash . NSLocalFile::getFileNameStripped( $this->newName );
	}

Change 763500 had a related patch set uploaded (by Llanddewi; author: Llanddewi):

[mediawiki/extensions/NSFileRepo@master] component: solves debug error when moving file to a different namespace

https://gerrit.wikimedia.org/r/763500

Change 763983 had a related patch set uploaded (by Robert Vogel; author: Llanddewi):

[mediawiki/extensions/NSFileRepo@REL1_35] component: solves debug error when moving file to a different namespace

https://gerrit.wikimedia.org/r/763983

Change 763500 merged by jenkins-bot:

[mediawiki/extensions/NSFileRepo@master] component: solves debug error when moving file to a different namespace

https://gerrit.wikimedia.org/r/763500

Thanks for the contribution. I have merged it into master. Currently checking LTS branch REL1_35.

Change 763983 merged by jenkins-bot:

[mediawiki/extensions/NSFileRepo@REL1_35] component: solves debug error when moving file to a different namespace

https://gerrit.wikimedia.org/r/763983