Presumably that one link is to the publisher's own website which can then offer any number of payment mechanisms, e.g. Stripe, PayPal, or directly entering a credit card number.
I wonder is it possible to put a link on both login page and settings/subscription page.
But can the publisher link back to the app after payment?
Yes. This is already a feature.
And is the link automatically coupled to the account in the app?
That's up to the developer to implement, but totally possible.