A hospital district management contractor in its management or operation of a hospital under a contract with a hospital district is considered a governmental unit for purposes of Chapters 101, 102, and 108, Civil Practice and Remedies Code, and any employee of the contractor is, while performing services under the contract for the benefit of the hospital, an employee of the hospital district for the purposes of Chapters 101, 102, and 108, Civil Practice and Remedies Code.