Canada is selective about immigrants (they have a points system), so all the things you call out are accounted for in their model - they bring in those their country needs. And from what I see from down south, they benefit a lot from it.
I would assume that if a population remains stable as a result of migration, that as many people are leaving houses as entering them, and there shouldn't be substantial pressure on housing prices. I don't have specific data for this.
[1] https://www.seattletimes.com/business/real-estate/vancouver-...
(Though we'd have to be really mad to replace it with a lottery...)