First thing I should say is it only relates to the new tyre physics system and not the public version, in any way.
They are supposed to be an estimate of slip angle and slip ratio at the peak of lateral or longitudinal force. But it is just an estimate based on an earlier version of the tyre model. In fact there is a comment beside the function:
// TYRE TODO - very inaccurate
This function is currently only used in these diagrams and in some estimates for AI drivers and keyboard steering. It's not actually used in the physics, although it should represent it to some extent.
It is based on a simple function with a few multiplications and a division. It doesn't take a reading from the actual output forces and really it shouldn't be displayed in the editor at all at this point.
Anyway, that function is supposed to report an increase in the estimated slip angle (and ratio) at the peak, as grip increases, and also as tread stiffness decreases.
That's what I'm seeing with the Formula XR rear tyres:
R1: mu 1.61 SA 1.8 SR 3.2
R2: mu 1.52 SA 1.3 SR 2.3
R3: mu 1.47 SA 1.0 SR 1.7
But that doesn't correspond with what you said. In this case the inaccurate formula predicts that grippier tyres will produce a wider slip angle at peak lateral force, which is what I would expect.