I need to create an pie chart from an image.
I'm really lost here. Hope someone knows
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Illustrator's 3D effect Extrude makes the thickness with no effort after you have the image slices as a group of flat shapes.
Trace, draw or purchase the needed shape. It must be a single path. Let it have a solid fill color and no stroke:
Draw above it a big pie chart which has the needed divisions as separate single vector paths.
This one is made by splitting a circle and applying Offset Path to get consistent gaps. Illustrator has a charting tool which divides a circle to wanted percentage wide sectors, but it's up to you to draw manually such divisions that the animal shape is divided to right looking proportions. Illustrator doesn't have a tool which splits say a rooster shape to sectors so that the sector areas have wanted predefined proportions. Or actually I do not know how it's in version 2024.
Separate with the Shape Builder tool or by using Pathfinder > Divide the needed splices of the shape. Give to them fill colors as you like.
You probably insert later some texts or numbers. Think in this phase how to make everything visible if there's some text on the final pie chart. Some random colors:
Group the pieces. Apply 3D extrusion effect, adjust the extrusion depth, perspective, viewing direction and light parameters. This example uses the Classic Extrude & Bevel version of the effect.
NOTE: There's nothing comparable available in Illustrator's rivals Inkscape and Affinity Designer. There one must draw the thickness manually or circulate the work through a 3D drawing program.
In your example the white numbers on the chart look like they are also on the top surface of the extruded shape. Distorting the numbers a little lower can be good enough. Applying 3D effect Rotate makes them possible to have also a perspective. Use the same view angle and perspective as you used for the extruded shape. In the next image the texts are only scaled vertically: