In the checkout editor, in header → cart Link the link is visible as well as in the preview, however on the website the link does not appear, only the logo, as can be seen in the screenshots.
I have already reset any styling customizations using the mutation checkoutBrandingUpsert
I tried looking for it on your current website but I don’t think your current website is on shopify.
Without looking at the website it would be impossible to comment anything. Let me know if you want to do a screenshare and debug it.