Typical business closure for New Year in Japan is Dec. 31 - Jan. 3. Jan. 4 is considered the first business day of the year. If Jan. 4 falls on Sat. or Sun. then the first business day is coming Monday from Jan. 4 and some businesses will extend closure till Monday in that case.
There are businesses open on Dec. 31, because of Dec. 31 is the day of preparation for New Year, technically not a day off. But often businesses will close early on Dec. 31.
Hope you will be able to visit Japan in New Year of 2023!