Way of the Househusband Part 2 will release on Netflix on October 7th, and will feature several more chapters from the manga, such as the chapter featuring the infamous rap battle, as well as Tatsu having his in-laws over for dinner.
Unlike the trailers for part 1, the trailer for part 2 seems to be much more upfront about the limited animation style of the anime. In Japan the series was marketed as more of a motion comic, which makes sense that some sequences straight up feature jumping from panel to panel.
Way of the Househusband follows The Immortal Tatsu, a legendary yakuza who left his old life to settle down and get married. The manga typically revolves around some permutation of the same gag- that he still views the world through Yakuza terms, painting a sinister light over simple household chores which he does with passion.
The manga had a large boom in popularity, leading to the publishers to shoot a short live-action commercial for it. The popularity of that then lead to the series getting its own live-action drama, before the anime adaptation was later announced.