Should public recruitment be used for internal recruitment in public institutions? If all employees are appointed by internal leaders, is it illegal?

Of course it is illegal. In addition, are you sure it is impossible to recruit establishment staff? If the unit recruits itself, if it does not pass the unified recruitment examination, will the establishment office, personnel bureau, finance bureau, and the competent department agree? The Staffing Office must have an administrative letter of introduction from the Human Resources and Social Security Bureau before recruiting someone to the staff, and the Finance Bureau must issue a joint letter from the competent department, the Staffing Office, and the Human Resources and Social Security Bureau if it wants to pay a new employee a salary. Is this what your unit can do? You are probably not recruiting staff, but contract workers.