Update: I was able to move forward with my project by diving in and learning how to achieve doing it by myself. I am using WordPress Auth-app-plugin to handle the “handshake” with my database application, but I understand that WordPress is working on making this part of its core.
With lots of these things, when you are an early adapter, things are harder to achieve. My guess is that over time, Zapier and its competitors and/or WordPress will make things easier.
All I can say from a personal point of view that I am disappointed with the lack of commitment from Zapier at this moment.