I am trying trying add someone as my legacy contact both on my Mac and on my iPhone and it does not work when I click on their name in Contacts.

I believe if you choose a Legacy Contact who already has an Apple ID, the procedure doesn't require that step and all you need to do is tap the contact.

If that contact does not have an Apple ID, you can click the prospective contact's email or phone number. Presumably adding someone lacking an Apple ID will require some steps that are not explained in that Apple Support document. It should.

When you are presented with your Contacts list and click or tap his name, does his Contacts card appear?

If so tap his email address in that card, and you will be able to proceed.

Lists is the only thing that comes up. How do I get Contacts to come up?