The birth rate has been declining in many places for decades, and that predates the current housing affordability crisis.
There has been however, for decades, mass movement of people towards cities. From what I’ve read, city dwellers statistically have smaller families than those in the country. Cities are of course much more expensive, smaller housing, more things to spend money on, etc.
Another thing that I think is a huge factor if you want to look at the people not having families, or the same size families, is women in the workplace and women’s education. There are a lot of women who prioritize a career over family. There are a lot of women who have careers and don’t financially need a husband and thus not likely to have a family. I’m no expert on this statistically, but I am pretty sure that I read that the more education a woman gets the less likely she is to have a large family.