In our shop wishdish.de we had some additional apps installed that we don’t use anymore so we deinstalled them. I think after that our checkout button did not work anymore, it only refreshed the cart page. I tried to reset the cart-template.liquid to the initial state but this did not fix the issue.
I think the app responsible for the mistake is CreativeR Store Pickup:https://apps.shopify.com/store-pickup-2?surface_detail=creativer+pickup&surface_inter_position=1&surface_intra_position=6&surface_type=search
At least a lot of its code is still visible in the template code.
Thanks for your help!