You mean Reuters is making stuff up? That's not possible. They interviewed like one person that says cost of living is high and they're considering moving.
I'm not even sure the cost of living is still surging. Gas is cheaper. Real estate is going sideways. At least in my personal experience it's stabilized.
More seriously. Canada had brain drain for some time. People leaving to the US e.g. I'm sure that's still happening. I think Trump being elected in the US slowed that somewhat. There's all sorts of reasons why people move from one country to another. Correlation, causation and all of that.
The Globe and Mail has an this headline:
"BoC Deputy Governor Gravelle says high immigration adding to housing inflation".
EDIT: Also immigrants leaving isn't that unusual. Immigration isn't for everyone. You might have family and friends behind. It might be hard to make new connections. Get a job. It's pretty cold here too.