UPDATE: you should try Gordon's proposal - he is an experienced PRO Blender user - i just started using Blender a few month ago...so scroll down to his professional answer.
repair your face orientation like this:
mesh -> normals -> recalculate outside
i know, the "moderators" here are very fast with closing questions although they appearantly didn't check your blend file.
I never saw something like this, but i found a "workaround" for you.
Check this video how you can "repair" it.
Essentially you can at least improve it by adding some loop cuts at the right positions.
So here is Gordons answer:
Solution is quite easy, the darker part has some "thickness" to it and smoothing goes around the edges. Not even deleting the solidifying faces helps. Autosmooth would normally take care of that, but if you enable it you see the "30°" is greyed out. That's because there is some custom Geometry Data on the object. Click on Clear Custom Split Normals Data to remove it and Autosmooth works as expected. I've made some screenshots for explanation, too. –