Is the rejection of a job applicant after the manager's approval considered "cutting off livelihoods" if the closest friend is slightly better qualified?

No human being can cut off a provision (rizq) that Allah has decreed for His servant. If your rejection of the applicant stems from your personal desire, then there is no sin upon you for that. However, if the matter requires you to assess his suitability for the job, then this must be taken into consideration.