Patents are registered separately by country, and there is no worldwide patent office. If Koreans want to register the Mid-Autumn Festival in the Korean Patent Office, there is no technical obstacle, but it is difficult to succeed, and even if the patent office accidentally registers successfully, the patent is untenable in court.
If you apply for intangible heritage, you can't apply for festivals, but unique celebrations can. The Mid-Autumn Festival celebration of the Han nationality is not the object that needs protection and assistance, and the priority should be relatively low.