Why does IAS decrease with lower air density if power is constant?
Because even with constant power, thrust decreases with velocity, also known as TAS.

Drag depends mainly on the dynamic pressure, which is what IAS represents, so if you had the same thrust, you'd have the same IAS too.

However a piston engine produces approximately constant power (if your RPM is in the optimal range), and power is thrust times velocity. So the turbocharger lets you have the same power in the less dense air, but because your true airspeed is higher, the thrust is a bit lower and therefore your (maximum attainable) indicated airspeed is as well.

And then there is the effect of RPM. Engine power (of any engine) is limited by RPM, growing up to some optimal speed and then declining (and then you get to the red line). If you have a fixed propeller, your available power grows with speed first as the RPM increases with decreasing effective pitch, but then you cross the optimum and the power starts reducing and then you hit the red line and have to retard the throttle. And effective pitch again depends on TAS.