Can a store or another website add people to my Podspun list?

Yes, by sending people to your website's signup page. It is at /signup on your website, for example https://yourdomain.com/signup, and it shows the same Join card your pop-up does. Use that address as the link behind the signup button on the other site. The person signs up there and is added the same way as any other signup on your website, with the email topics they chose. Adding ?join=1 to the end of any page address, for example https://yourdomain.com/?join=1, opens the Join pop-up over that page, which works too.

This works from a store on another service such as Shopify, a link in a bio, an email or a QR code. Make it a button that links to your website. A signup box that sits on the other website keeps the addresses in that service, because a form on another website cannot write into your Podspun list.

To bring across addresses another service has already collected, export them from that service as a CSV file and import the file under Contacts in Email Campaigns.