Unfortunately, your website is completely unavailing again because of 20 instantly running PHP processes in background (I even it not capable to load the frontend home page), but when I cloned it to my local PC and updated the Square extension to the latest version, I am unable to reproduce your problem: the error messages are correctly shown to the customers, see the screenshot:
I have made some improvements to the Square extension today, so try to upgrade the extension to the latest version: it could solve your problem.