How to retrieve a payment method on the client side?

After contacting Stripe directly, it was confirmed that that's just the way it is:

I think it's just an oversight that we didn't add one.

There are similar functions in the mobile SDK so I don't see why we shouldn't have it

There are no immediate plans to add the functionality back in in the very near future, so as a workaround, I will tunnel all the data through our backend(s).