Now the real question: Do people living in basement units in the developed world count?

I would argue yes, and this would easily raise the number by a few tens of millions.

They have to do more than just sleep underground. They would need to do some work or eat or something else other than just have a room that is underground.

According to the resolution in another question by @cloudprism, yaodong residents count as underground population and they number in tens of millions.

https://en.wikipedia.org/wiki/Yaodong

@SarkanyVar About 40 million residents, according to https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://htschool.hindustantimes.com/editorsdesk/knowledge-vine/yaodong-the-cave-homes-of-china-that-co-exist-with-modern-high-tech-buildings%3Famp%3D1&ved=2ahUKEwjC99qA3L6AAxVwGhAIHTXmBnQQFnoECAwQBQ&usg=AOvVaw2NAk_Ikzw1WE6K0oCXY8m8.

Even with a full 2 generations of one child policies you would still end up with 10 million in 2040 as a very conservative estimate.