Its not blaming immigrants, that is a common tactic used by lobbyists and politicians to shut down discussion. Its simply what the BoC and our institutions say.

https://www.canada.ca/en/immigration-refugees-citizenship/corporate/reports-statistics/research/immigration-housing-prices-municipalities-canada.html#s6

The results show that, over the study period, the rise in the influx of new immigrants, who arrived in Canada within the past five years, on average, accounted for 11% of the rise in median house values and in median rents across municipalities with a population of at least 1,000. This association was notably more pronounced in larger municipalities. In the 53 municipalities with a population exceeding 100,000, which together attracted over 80% of new immigrants, the rise in new immigrants accounted for 21% of the overall increase in median house values and 13% of the increase in median rents. In these large municipalities, the effect on house values tended to be larger than on rents, possibly due to rent control policies in many provinces that can cap rent increases for certain properties (Gorski, 2023).

https://www.bankofcanada.ca/2023/12/staff-analytical-note-2023-17/

The wage one is harder to quantify due to inflation, wages would have gone up far faster like in the US, but overall wages still rose. Wages just bought far less and people who dont own inflation hedged assets are far poorer on a per capita basis.