The establishment of teachers means that the Education Bureau has gone through all the formalities for you. As long as you don't resign, you will enjoy all the benefits until you die. That's an iron rice bowl.
Entering public schools requires examination and compilation, which belongs to the establishment of teachers, and entering private schools belongs to the non-establishment of teachers. Teachers must pass the examinations organized by relevant departments and become teachers in the establishment after being hired, that is, "personnel in the establishment". If the school becomes "supernumerary" because of the overstaffing after employment, it is actually what we commonly call "on-the-job" personnel, and it has no influence on them. You can wait until there is a vacancy before joining the job. Teachers in editing are career editors, that is, teachers in editing are staff of public institutions. Non-editorial teachers are temporary or contract workers.
The full name of career establishment is career establishment, mainly engaged in professional and technical posts or work-related posts. Whether it is a public institution or an administrative unit, the staff of these positions are career establishment. The staffing of public institutions is generally non-civil service, and its funds are generally paid by the state. The purpose of starting a business is to create or improve production conditions, enhance social welfare and meet people's cultural, educational and health needs, and its funds are generally compiled by the personnel used by the units that spend the state's business expenses.