You are correct. There is no mechanism to have a W2 with zero in boxes 1,3, and 5 and a housing allowance in box 14. Box 14 is typically for an employer to use for informational purposes only. The housing allowance amount in box 14 is information for the clergy employee to use for self-employment taxes.
Therefore, since the pastor is not an employee (no salary) then the church can report the housing allowance on a form 1099-NEC. This is the form to report payment for services to a non-employee. The pastor then uses the 1099-NEC to report the income as self-employment income.
Here is a link to the Form 1099-NEC instructions.
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