[Vuejs]-How to implement payments in chrome extension

For PayPal you can use API calls to activate a subscription from a server.

This gives you reliable server-side notification that a subscription is started.

To be notified of actual payment transactions on the subscription, which typically start the following day and repeat on its cycle, you need a webhook listener for the event PAYMENT.SALE.COMPLETED

You could also try to use the ExtensionPay service which gives you a simple API to take payments in your extension.