it depends on US law about adoption.
if an adopted child has no way to escape from getting US nationality (i.e an adopted child will have US nationality automatically in the adoption process), Japanese government may accept dual nationality until you become an adult.
1. the updating your koseki is your duty. there is a penalty, if you don't make your koseki newest.
2. your koseki was not removed (is present somewhere).
3. your koseki was separated from your mother(?)'s koseki and they made a new koseki, in which only you are a member.
4. since koseki is the record of Japanese nationality holders. you only can get an official copy of koseki. "without koseki" = "not koseki holder" = "not a Japanese"
5. koseki is maintained at city halls. not by Japanese government.
6. if you want to have a copy of your koseki, you need to know your "address", where your koseki is there. also, you need to know your name (written in Japanese) and your birth date.
7. you can ask パスポート申請情報開示請求, disclosure request of your information about passport application. I don't know the embassy may help it or not (probably not)
https://www.mofa.go.jp/mofaj/public/johokokai/passport/index.html旅券(パスポート)の発給申請書の写し
if you have an expired passport, it may be helpful.
a typical example is:
https://www.pref.kanagawa.jp/osirase/02/2315/img/form_ippan_omote.png(1) : your Japanese name
(3) : your "address" where your koseki is there.
8. since the information is private, only the passport holder can do that.
when the embassy does not help you, you may hire a professional (probably from abroad), who can do it legally instead of you.