Do the polar curves have large differences in takeoff than in landing? I was wondering if the polar curve has differences in the takeoff due to the smaller extension of the flaps (this is half that in the landing) that changes the AOA for $ C_ {la} = 0 $. In addition, should I calculate the landing polar on approach?
The $C_L(\alpha)$ curve changes with flap/slat extension, so it should logically follow that the polar will also change, since the induced drag depends on the lift.

Furthermore the parasite drag will most likely change as well due to a changing airfoil surface.

So yes, the polar needs to be recalculated for all flight configurations.