Proximity (raster distance) using ellipsoidal distance

Question

When creating a proximity layer, based on some rastered features, I noticed that the values in that layer seem to represent Cartesian distances.

Is it possible to generate a proximity layer using the ellipsoidal distance to those rastered features?

I used the following tool: Raster -> Analysis -> Proximity (Raster Distance)

In the images below I measure the distance between a corner of the feature and some city center to be around 3km.

However the generated proximity layer reports a distance of around 5km here. This happens to be identical to the Cartesian distance.

I am new to these techniques, so there might have been a few steps that I missed.