The internal "Shape__Area" field is based on the spatial reference of the layer, and is purely two-dimensional.
It's important to note that the built-in measurement tool is using a geodetic measurement, which is not how the internal field calculates. It's easier to see if you zoom way, way out and go near one of the poles. Here's a polygon in Web Mercator, showing the built-in area, the Arcade 2D area, and the geodetic area:
And here's me trying to measure the same shape. Note that the measurement matches the geodetic value from earlier:
The geodetic measurement is taking into account the curvature of the earth and the latitude of my features. Try it yourself, use the measurement widget near either of the poles. You'll see that your two-point lines get automatically curved.