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I'm able to use $entity successfully in display code entered into the field configuration form directly. However, attempting to use $entity in a custom display function results in an error indicating that $entity is undefined. Any chance it can be made available to custom display functions?
Additionally, while working on this, I found that:
computed_field_field_job_posting_number_display($field, $entity_field_item, $entity_lang, $langcode)
...resulted in errors indicating that $entity_lang and $langcode were undefined. I had to remove them from the function's arguments list.