It turns out this error was caused by a misconfiguration of the SSL certificate at the web host's end.
After getting the error on Exp:resso Store pages using https, I tested a page load of the home page (a non Store page) and got the same error. I concluded it wasn't an Exp:resso Store specific issue.
I eliminated htaccess as the source of the error by loading the page with an empty .htaccess file.
I then uploaded a test html file and tested page loads with http and https. https still failed and showed the EE error. This page load of a non-EE page shouldn't show an EE error ever... What the heck? So this wasn't an EE error.
I concluded this was a server issue and emailed the host. They fixed the misconfiguration promptly.