Blender's smoothing algorithm will, by default, round off all edges. Even edges you may want to keep sharp. To prevent this, we need to tell it which edges we want to preserve by creasing them.
Lets start off by temporarily disabling the Subdivision Surface modifier. You can do this by clicking the eyeball icon.
Now lets select the edges we want to crease. An easy way to do this is by going to Select > Sharp Edges. This will select all edges with a sharp angle.
Play with the sharpness threshold until it looks like it has most of the important edges. It does not have to be perfect. We can add or remove more later. This is just to give you a good starting point.
Crease the edges by pressing SHIFT+E then type 1.0 and press ENTER.
To uncrease an edge, you would type -1.0 instead
You can now unhide the modifier to see how it looks, then go back and crease/uncrease more edges as needed.
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