Assuming you’re letting the user click a button in the details view of each row, you can use an Integromat scenario to do this.
Add an Integromat webhook to send data from Glide, I assume you just need to send the email of the user and the “Shopping List Items”.
Then in Integromat, add an iterator that runs on a split from the Shopping List Items. Every iteration will add a row to your “Shopping List” sheet with the user’s email and the splitted item.