They own Purolator:

Canada Post owns 91 percent of Purolator, a major player in the domestic parcel market. Over the past four years, Purolator’s revenues have averaged approximately $2.5 billion, indicating that Canada Post is far from broke. If Canada Post held exclusive rights to parcel delivery—as it does for letters—it would easily break even.

As the article describes: there are a bunch of gig work companies whose costs are significantly lower than Canada Posts. Straight competition won't work.

Why not nationalize delivery services?

That would require an act of Parliament. Our last dozen or so governments have been pro-business, so that seems unlikely. But we can dream.

Canada post missed the bus when they didn’t find a way to pivot and use their infrastructure to create a delivery system for Internet packages. Now they have to try play catch up.

Canada Post exists as a Crown Corporation under a specific mandate; I don't think they could just pivot to become an internet service provider on their own