Thank you for reaching out and posting this question!
I’ve taken a look at your shop (landrace-bakery.myshopify.com) and I’m not seeing the same local delivery or store pickup options on the cart page. Based on your screenshot, it does look like you’re using a third-party app. Just to confirm, did you uninstall the app already?
It is possible that the cart/checkout can get stuck when an installation of a third-party app wasn’t done correctly. Nevertheless, if you’d like to get the app working, then the app developer is always available to assist you. You can reach out to the developer directly through the contact information found in the Support section of their app’s page.
That being said, it does look like you’re using the native local pickup at the moment. If you require any assistance with the local pickup/delivery, then this is something that we’d be happy to help you with. While we’re not able to provide account-specific support via the Shopify Community at this time, we’d be happy to continue assisting you through live chat, email, or callback. Please visit the Shopify Help Center and log in to your account to create a support request.