Late reply here, though yeah. The anime is based off these chapters. Though the author has a sequel for this story, called "Let's go to family restaurant." Or "Famiresu Iko." The author also has a new work that will be released next year! Which MIGHT be a third part of the series. Though no one knows what type of story it is :D
The company that serialized "Let's Go to the Family Restaurant" manga, Comic Beam, revealed in a March issue that the author, Yama Wayama, plans to launch her next work in 2027. It's been a while, so I can find the original magazine issue. Though here's an English article that might have it.
https://www.animenewsnetwork.com/daily-briefs/2026-02-13/let-go-karaoke-s-yama-wayama-plans-to-launch-new-work-in-2027/.234142

I just watch the anime and I really want to know if there's a manga and is it really 3 chaps?...