Why is the delta connection called constant kilowatt and the star connection called constant torque in pole changing motors?
When the connections are changed, the windings are re-distributed so that the motor has a different number of poles. If the high speed connection has 4 poles and the low speed connection has 6 poles, the high speed is 1.5 X the high speed. For a 6 to 8 pole change, the high speed is 1.33 X the low speed.

In diagram 1, the low speed has two halves of each phase winding connected in parallel and connected to power in a wye configuration. In that configuration, full voltage is applied to each half-winding. That would correspond to rated torque. For the high speed connection, the full winding is connected to power in a delta configuration. That multiplies the voltage by the square root of 3, but applied to the full winding, each half-winding receives 0.867 of the voltage applied at low speed. The torque capability is approximately proportional to voltage squared, so 0.867^2 = 0.75 of rated torque. So the high speed power capability is 0.75 X 1.5 = 1.125 X the low speed capability for the 4/6 pole motor and 0.75 X 1.33 = 1.0 X the low speed capability for the 6/8 pole motor.

I believe that either motor would be sold as a constant power motor.

The other winding configurations can be similarly analyzed. It is likely that not every pole combination will be available for every torque vs. speed option.