It's a cause-effect chain. The house price inflation lowers marriage rates and raises the economic burden on couples, which lowers birth rates, which incentivizes mass migration, to replace the missing children.
But economically crushing your local populace and then subsidizing foreigners to replace them, is next-level political perversion, IMO. And a lot of us migrants are now locals, and we're also getting crushed. So, you know, now they have to replace our missing offspring, too... It never ends.