Canada has a housing crisis and rents are sky high so you will find the costs for everything in Canada higher than the US. Have you figured out if you are eligible for Express Entry or PNPs to immigrate? What is your CRS score? Work permit is not an option.
Focus on researching immigration programs if you want to move to Canada. A work permit is not going to be approved for Canada with a pending refugee claim in the US.
If you have an approved work permit, you should be good to enter Canada now. Ultimately it's your choice.
I agree with @scylla's point above - but I would just emphasize that if anything should happen (like your PR application in Canada is refused and you can't extend your work permit, or some other scenarios), you would/could end up with the need to leave Canada and inability to return to the USA (the latter point probably obvious). Or without the ability to work.
Would add that it is extremely unusual to be able to get a WP with an asylum claim open in the US. Although you have an approved work permit you could still be denied entry into Canada because you won’t be able to prove that you have strong ties to your home country and will return if you lose your WP. Safest way to come to Canada knowing you should be able to remain without issue is being approved for PR.
just an update. Went to canada. Passing through immigration was smooth. They were very friendly. Only asked where I will be working just for confirmation and my work permit was issued.
@omasan Thanks for your response. I’m currently considering PNP as I’m eligible for this PR route
