I am not really certain but that probably doesn't refer to adopting a child. It refers to Sei adopting Ryou. That way, he will be added to his family registry without being married. I think that's what he meant cause I have seen it in a lot of manga but still I could be wrong.
I can confirm this is most definitely what they mean. Because if they have no connection to each other in case one would end up in hospital for example they wouldnt have the right to visit them. Hence the adoption.
Wait, I’m confused. If Sei adopts Ryou, what happens to his biological family? Do they normally allow adoption beyond the age of majority?
so same-sex couples are not allowed to get married, but they're allowed to adopt together in japan? that's odd