Like the recycle bin on JS informs the site owner about purchasing?

It would be strange if the basket is left on the client and not stored anywhere on the website or another store. Should be the same as the store to process the order.
On the back end should be receiving the script from your JavaScript data and bringing them to the database/file/other server storage for further processing. The actual implementation of the functionality - the conscience of the developer, how to send data to the server have to understand any web developer entry level.

The client clicked send, the server made receiver( XS what language do you have a server:) ) accepted the request, the data recorded in the database.

Services if you meant API - Yes!