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.