Yeah the model doesn’t deform with shade smooth, it smooths the shading based on the direction of the normals. This looks like a classic case of the inconsistent normals as Spikey mentioned.
If you are trying to smooth the sharp edges, you can use a Subdivision Surface Modifier, you will need to add some holding edges to maintain the shape though.
You can do this manually, or you could use a Bevel Modifier above the Subdivision Surface in the modifier stack, adjusting the settings to your liking. But make sure your scale is applied to use meaningful values.
