The Bergmann purchased by Imperial Japanese Navy were mainly the 7.63mm Mauser version of SIG M1920, and it is highly unlikely that 7.65mm Parabellum version was purchased.
The 7.65mm version of SIG M1920 was used primarily in Northern Europe due to ammunition supply concerns, and was not widely used in Asia where 7.65mm Parabellum was not widely available.
In China, copies of the SIG M1920 have been made mainly in Shanghai and Nanjing since 1926, and from 1927, improved models with changed magazine mounting positions were produced in Dagu and Qingdao. Early copies of the SIG M1920 produced in Shanghai, Nanjing, Hanyang, etc. had a 7.65mm caliber, so it is possible that the Japanese military had captured and used it…
The MP-28 (7.65) was probably intended for the Chinese Bergmann.
It is true that some Shanghai and Gongxian Bergmans have 快慢機 (=selector) in imitation of the MP-28, but it is doubtful whether there were any individuals with both the 7.65mm caliber and the selector.
↓If you understand Japanese, please refer to this.