Simply adding a ``setDeleted()`` method and ``$deleted`` property to the Extbase domain model is not sufficient.
You also have to add the ``deleted`` column to the table's TCA ``columns`` array.

Otherwise Extabase's "Persistence Backend" will decide that the property is not ``isPersistableProperty()``, and skip over it.

Links:

- https://stackoverflow.com/questions/79841935/extbase-domain-model-version-property-is-not-stored-in-database
- https://github.com/TYPO3-Documentation/TYPO3CMS-Reference-CoreApi/pull/6479