Canada

The issue is that you're conflating patriotism with nationalism. Patriotism is loving your country while nationalism is thinking your country is superior to other countries. You can live and work in another country while still loving the country you came from. But if you believe your country is superior to other countries it would be hypocritical to want to go to another country.

So you are correct to think that wanting to go to the EU doesn't align with nationalism. What you're missing is that Canadians aren't being nationalistic, we're being patriotic. We're against the US because the US is trying to assert dominance over our country, and that's an existential threat to something we love. Elbows up is a reaction to that threat.

The EU on the other hand is not an existential threat to Canada. In fact a partnership with the EU will make both Canada and the EU more resilient against external threats to both. The EU doesn't want us to stop being Canadian, and the very nature of the EU is multicultural and multilingual, so a Canadian could live and work there while being respected as a Canadian. This may not be the case in other parts of the world.

You're also thinking the immigration policy is about some nationalistic cultural thing. It's more of an economic consideration. Right now there's a housing crisis in Canada and we're in an economic crisis (because of you know who). It's not economically feasible to have significantly more inflow of people than outflow right now. An open immigration policy with the EU isn't going to happen tomorrow, and the housing situation and the relative inflow and outflow would be considered before adopting that kind of policy.