The problem boils down to the lack of equivalence between a site and an origin. The article explains how https://app.example.com and https://marketing.example.com may sit at very different trust levels, but are considered the same site by the browser. You don't want https://marketing.example.com to be able to make requests to https://app.example.com with your authentication cookies, but SameSite wouldn't prevent that.

This doesn't match my experience. What am I doing different?

Example I set SameSite=Strict on www.edoceo.com and then visiting app.edoceo.com the cookie is not there? They are different sites, different origins. And the cookie is set to the domain (ie: host, ie: www.edoceo.com)