The Verdict: Not eligible
Japan has no residence status for the same-sex partner of a Japanese national, even with a marriage made abroad. Look at our Skilled Migration, Golden Visa and Diaspora & Religious Return routes for Japan instead.
Japan does not recognise same-sex marriage. Since 2013 it has granted a status to the same-sex spouse of a foreign resident where both partners' countries recognise the marriage, but expressly not where one partner is Japanese. Courts have been asked to look at that gap; immigration practice has not changed.
Municipal partnership certificates are local recognition schemes. They do not create a right to live in Japan, which is national law.
What remains is a route of your own: a work status with a qualifying job offer, a business or start-up status, or Long-Term Resident status if you have Japanese ancestry within three generations.