Does Japan National Tax Agency also let you see other details - like parent company of the entity, or any other information? That's provided in countries like India or Vietnam in their corporate ministries/departments
Not from the tax agency. For a KK you can get a list of investors from the legal affairs bureau for a small charge, and for any kind of company you can get a history of who has ever been representative director or equivalent. AIUI it's possible to have a "silent partner" setup where you have a partnership or GK and the representative is a lawyer rather than the person actually operating and profiting from the company, but there always has to be at least one publicly named representative.
METI (Ministry of Economy, Trade and Industry) has a portal to potentially display that information, but for private companies it may be missing, and thus the results may be no better than NTA's records: https://info.gbiz.go.jp/
Public entities (which Big River Services Japan is not) can be searched through the JPX (Tokyo Stock Exchange): https://www2.jpx.co.jp/tseHpFront/CGK020010Action.do