Normally, you would see a custom prompt or a (native) browser prompt on a store to ask the visitor permission for push notifications. But on some stores you can see a popup asking for permission instead, like so:
This happens when a store doesn't have the service worker file available. This would rarely happen on a normal Shopify store (using Shopify frontend) as PushOwl automatically creates this file on the store. So you don't need to worry about this file.
But on a headless store, where PushOwl has to be set up manually, the store might not have been able to host the service worker file on their domain (Refer Step 2 here). In such a case, it's not possible to ask native permission on the main domain. So PushOwl opens a popup and asks permission inside it.
Note: Further features likes automations, campaign sending, etc work as usual after a visitor subscribes.