Influence of tire breadth on cornering
My guess is the squeak:


Does not happen on all road surfaces
Occurs while turning due to friction between the tire and the road generated during a turn.
Is not related to tire width or frame geometry


Going out on a limb...
The squeak will go away as the "shine" is worn off your tires.
You might be able to change or entirely get rid of the sound by changing tire pressure.

In the original post nothing is mentioned concerning reduced traction or ride issues.
Tire pressure should be adjusted to gain the best traction and ride - not to get rid of this sound.