If I Buy travel insurance Do I still have to file a claim with the airline?

I’ve never purchased travel insurance before but am going on a 2 month long trip and would feel way more comfortable with a little more protection than just my credit card offers.

I know airlines have to cover you for about 2k due to the Montreal convention but from experience they fight tooth and nail to not cover cost. if I pay for travel insurance can I ignore the airline completely if something goes wrong or do I have to still file a claim and go through the month long battle to get my stuff back/reimbursed before travel insurance kicks in.

If it helps I’m looking at a Faye plan that would cost me around 300. I think it’s worth it for the piece of mind but if you guys have other suggestions I’m open to that too.