This is very valuable data! First, I can confirm that the AI is actually right this time: 16in @ 25ft is 3.06 degrees, and 3ft @ 25ft is 6.87 degrees.
We know a good deal about these lights: first, they use emitters with around 4mm^2 LES, which gives an “effective” emitter radius of 1.13mm (a circle of equal area). The GT mini’s reflector has 43mm diameter and 40mm depth, and the S6’s reflector looks around 19mm diameter and 19mm height.
Plugging in these numbers, my formula predicts 2.51 degrees for the GT mini, and 5.45 degrees for the S6, both on the low side. Part of this could be due to the square shape of the emitter causing the hotspot to have an ill-defined boundary.
If I took the radius to be the smallest circumscribing circle around the emitter, i.e., 1.41mm, I would instead get 3.13 and 6.80 degrees, which is pretty good compared to 3.06 and 6.87. For square emitters, maybe circumscribing radius is better than “effective” radius as a predictor for beam behavior.