Do graduate students who teach in public primary schools in Shenzhen have to take the exam?

Don't. According to the Announcement on Matters Related to the Open Recruitment of Teachers in Shenzhen Municipal Primary and Secondary Schools in May 2023, the candidates should meet the requirements of: fresh graduates from ordinary colleges and universities who graduated from September 2022 1 to August 3, 2023/,undergraduate graduates with nationally recognized academic qualifications, and Hong Kong and Macao residents who meet the requirements stipulated in the Administrative Measures for Open Recruitment of Hong Kong and Macao Residents in Guangdong-Hong Kong-Macao Greater Bay Area Institutions and the recruitment announcement.