They allow anyone over 50 to join, regardless of job status. I think they have acknowledged that most of us can’t just stop working at a specific age and that we will probably seek other jobs even after we retire from our previous job.

Oh, I know. They started sending me "You're almost old enough to join AARP" shit when I was still in my 40s. I was being somewhat facetious, but it's still a pretty sad state of affairs that "retired" people can't actually be... retired.