We are working with a merchant to move their existing subscriptions from a subscription app using Shopify's checkout to our app.
I would like to know if we can use existing customer payment methods for contracts we create / migrate in our app. Are there any better ways to migrate subscription contracts from one app to the other?
Interesting question. I don't know if anyone has asked this before. Unfortunately, I'm relatively new to this area, and most of the folks on my team are gone for the day. I'll try to get an answer for you tomorrow (Thursday) Pacific Time.
I assume you've seen this guide (although I believe you're asking for a different migration, perhaps it has some clues): https://shopify.dev/apps/subscriptions/migrate/contracts.