A second part has been announced – https://www.cbr.com/netflix-way-of-the-househusband-part-2/ – and anime and J-drama series generally use continuous numbering, so are all one season in TMDb's definition of one.

Whether the part 2 episodes are allowed to be added when the number of new episodes and the numbering of them aren't know, I'm not so sure about.

We can add the second season (or even more episodes to season 1, although I disagree here) when they are out – for now the newly added episodes are definitely wrong.