I found on the Internet that the application for settling in Hong Kong has been approved. Do I need to wait for the call to go through the immigration formalities here as soon as possible?

If the approval is found on the website of the Hong Kong Immigration Department, you have to wait for the official approval from the Immigration Department, usually by mail, and then go to the Exit-Entry Administration with the endorsement documents to apply for exit documents and endorsements. If you find that the website of the public security organ has been approved, you can wait for telephone notification. If you don't notice for a week, you can directly bring your ID card to the Exit-Entry Administration Office for enquiry.