How do I create an app-specific password for iCloud?

Solution 1:

The missing information was provided by @GordonDavisson (and if he wants to post an answer I will accept his instead of mine):

To generate and use app-specific passwords, your Apple ID must be protected with two-factor authentication.

This is actually on the Apple Help page, but oddly not included in the section "How to generate an app-specific password" (even though it was the missing step for exactly that question) but instead buried between an explanation of what an app-specific password is (which was of no value to me) and fine print about different OS versions. I used the headers to skip right to the relevant information (which is what headers are generally for) and didn't guess that a critical piece of information would be placed elsewhere.

Solution 2:

It does exist, exactly where the not-outdated-at-all help information says it is.

The support article you link says:

Sign in to your Apple ID account page. In the Security section, click Generate Password below App-Specific Passwords. Follow the steps on your screen. After you generate your app-specific password, enter or paste it into the password field of the app as you would normally.

Doing this leads you to a page that looks like this:

And there you can create all the app-specific passwords you like.