How do I change the card I pay with?

Your plan is part of your Shopify bill, so it is paid with whatever pays that bill. You change it in your Shopify admin, under Settings and then Billing. nouz never sees your card. That is also why no card goes into nouz when you start the trial. In nouz, open Settings, then Billing, and click Open Shopify billing to go straight to that page.

The new card pays your next Shopify bill, and nouz with it. If a payment has already failed, pay the open bill in your Shopify admin, and nouz carries on as soon as Shopify has the money.