How likely is it that a utility model patent will be authorized after receiving the acceptance notice? How long does it take to know that it is authorized?

There is no necessary connection between getting the acceptance notice and authorization. The acceptance notice can only indicate that the submitted materials meet the acceptance conditions, the patent office will accept it and start the examination;

As for authorization, then It depends on whether the technical solution of the patent application is an unauthorized object and whether it meets substantive conditions such as novelty, creativity, and practicality;

Generally, if a utility model application meets the authorization conditions, it will take about half a year from acceptance to authorization. or so time.