There's a lot of jurisdictional overlap when it comes to housing, but Canada certainly does have a federal Minister of Housing, Infrastructure and Communities,

There's a lot of jurisdictional overlap when it comes to housing, but Canada certainly does have a federal Minister of Housing, Infrastructure and Communities, the office of which is currently occupied by Sean Fraser (who was formerly the immigration minister). But even if housing were entirely out of the federal government's hands, that wouldn't be an obstacle to them mathematically linking immigration targets to measured housing builds; they can link it to any variable they want to, even the weather on Mars.