Satoshi was born on an island off the coast of Japan, magically surrounded by a protective barrier to keep outsiders away. He is a samurai and Yamabushi, he protects the people of his village while also residing in a carved-out cave in the mountains. His father being a great Daimyo, he balances his noble upbringing with his enlightened lifestyle.

He is very spiritually trained and has ascended to achieve immortality. He was also born with magical powers, as one of the seven colored guardians, he is the blue fish- which means he can transform fully into a fish or halfway into a mermaid- or really anywhere in between.

He is married to Reznor, who he met traveling through the dream state, and they have three children: Ena (1893), Hanako (1972), and Shiori (2020).

Why does he have tattoos? 💙

So in Edo Japan, unemploymed samurai bandits would sometimes attack random people, so groups of people (Machi-Yakko) from villages would designate themselves as vigilantes and protectiors and get tattoos to seem more intimidating to the attackers
These people are thought of as the precursor to the Yakuza but obviously different in many many ways

Satoshi protects his village in a similar way, from any outside force that may try to get in, or magical inhabitants on the island

So no, he is not affiliated with the Yakuza, he is before their time and lives on a separate island anyways that is cut off from mainland Japan.