Boomer zoning laws do affect housing supply by reducing supply.
Immigration affects housing demand by increasing demand. These are both effects. They are both bad.
The solution options are: 1. Destroy zoning and keep immigration the same and go full Favela mode 2. 0 out immigration and keep having nice, but too expensive houses 3. address both problems and absolutely crater housing prices, thus giving the youth a place to grow and have families.
We do need to address both sides of the issue. Don't forget that there is both Supply, and Demand for any economic item.