Issue #3617729 by benstallings: Don't use storage as a class property

Ben Stallingsrequested to merge
issue/taxonomy_machine_name-3617729:3617729-dont-use-storage into 2.0.x

Inject the entity type manager instead and call getStorage() at the call site, per PHPStan's drupal.entityStoragePropertyAssignment and drupal.entityStorageDirectInjection rules.

Co-Authored-By: Claude Sonnet 5 noreply@anthropic.com

Closes #3617729

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