Nico Williams is still very young and he has a lot of time to upgrade his career with a bigger club. At the moment he can feel that he owns something from Bilbao and want to contribute something more for the club, like paying back what the club helped him so far. Anyway soon he will no longer feel Bilbao is a good enough club for his career. Playing with his brother in Bilbao is good but in future, their player career must go to different directions depends on their talent, ambition and given opportunities from big clubs.
I think Nico Williams has a personal reason why he still chooses to stay in Bilbao. And it seems one of them is because his brother also plays for Bilbao. In addition, as you said, Nico Williams feels he has to contribute to the club that has given him a lot of playing time to become one of the young stars in the world. I think Nico will play one or two more seasons in Bilbao before deciding to move to another club. If he can consistently maintain his performance, there will always be a big team that will want to recruit him every season.