There was an error in the App Store. Please try again later.

I have an old Macbook Pro I am trying to upgrade from Mac OS X 10.7.5. I want to get El Capitan, 10.11.x. I have found this page:

https://support.apple.com/en-us/HT206886

Which says how to do it and includes a link that opens that page in the App Store. When I try and "Get" El Capitan, I get the error:

There was an error in the App Store. Please try again later.

and then

"Software Update Required

To make changes to your payment information, you need to upgrade your Mac to the latest version of macOS."

Well, duh. Yes, I am trying to update my software, Apple.

I have verified that my payment information is up to date with a valid card. As suggested elsewhere, I signed in to iTunes separately, and while I no longer am asked to sign in in the App Store, I still get the above message.

How do I do this?