In Illustrator, I have an object that is curved and which I created with extrude and bevel, and then Object⇾Expand.
Is there a way to now change the color of the object and keep the shading of Extrude and Bevel tools?
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If you can accept a single color with no hue nor saturation variety you get it easily by inserting a top shape which colorizes the original below. An example:
The shape to be extruded
Extruded shape, Expand Appearance is applied
Clipping mask released, ungrouped 4 times, united to one item by applying Pathfinder panel's Unite
New fill color selected
Copies of (2) and (4) are aligned, (4) is on the top and has got blending mode Color.
Blending modes are selected in the transparency panel. It opens automatically if one clicks "Opacity" in the appearance panel. Blending mode Color applies the hue and saturation of the top object, the brightness variations of the bottom object stay. Try also other blending modes, at least Overlay, Color Burn, and Hard light. Some of them may give an useful result.
More possiblities can be got by using color editing, but that's quite limited in my legacy Illustrator, so I skip it. Hopefully someone shows what's possible in modern Illustrator.
I have Edit > Edit Colors > Recolor, but there's no other global adjustments than brightness. The lack of global adjustments and the high number of the splinters in the expanded shape makes color editing very difficult.
Altering contrast without color editing:
You can reduce the contrast by adding a single color (=united) copy on top with blending mode normal. Reduce the opacity to make original brightness variations partially visible.
Increase the contrast with blending mode Hard Light:
The expanded shape in the left is duplicated (=copy, paste in place) and the top version has got blending mode Hard light. It brightens bright and darkens dark. Applying the trick twice doubles it. Reducing the opacity of the top object reduces the effect.
Rasterizing: Copy and paste the expanded object as pixels to an empty image in Photoshop and use all Photoshop's power to colorize and change the contrast. Then you can save the result as PNG or PSD and place it to Illustrator as a raster image. Copying and pasting back to Illustrator removes the transparency, so save and place!
You do not lose any quality if you know beforehand what's the biggest size of the image and the image in Photoshop has high enough pixel dimensions. Most of us avoid this route because rasterizing removes the free scalability.
Not asked: The most powerful way to to get a new color is to recolor the original shape and extrude again, maybe with adjusted light settings in the extrusion dialog. I guess the original is now unavailable or there's so many extruded and expanded objects that the questioner searches something easier than guessing the right extrusion settings for everyone.