Eu usaria school administrator.

As a colleague already pointed out on the Discussion Board, it depends on whether you are referring to a person or the knowledge. If it's a person, both "school manager" and "school administrator" are used in American English. If it's the knowledge, "school management" would be a better translation.

Example Sentences

From the Virginia State Law Portal:
"A school manager is licensed to administer noninstructional responsibilities in an educational setting. For example, a school manager is restricted from evaluating teachers, supervising instruction, developing and evaluating curriculum, and serving as a school's student disciplinarian." https://law.lis.virginia.gov/admincode/title8/agency20/chapt...

From a California School District's website:
"HIGH SCHOOL MANAGER
A. PRIMARY FUNCTION

Under supervision, to be responsible for the food service operation; to count and prepare for deposition of food service receipts; to enter meal count data; and to do related work as required consistent with job description.
https://www.mynhusd.org/apps/pages/index.jsp?uREC_ID=428020&...

"Management" used in the sense of "managers":
"The school’s management will take steps so far as is reasonably practicable to ensure that the workplace is a safe and healthy environment in which its employees, pupils, contractors and other persons affected by the school operations can work." https://resources.finalsite.net/images/v1557482204/theryleys...

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