Just launched at least 15 years old CorelDraw 8 in a legacy machine. This problem was a natural test for it. The result: No in this case useful 3D tools existed. But manual tracing your image with the pen tool was not at all difficult. The background shapes especially can be coarse because only the visible lines must fit.
The foreground shapes drawn, united and filled with a radial gradient:
The rest of the shapes drawn, united, filled, moved to the background and all black strokes were removed:
CDR8's pen and curve editing tool feel very responsive for manual tracing works. Most difficult is to stay diciplined and not to add exessive control points. Too much points easily make the curve wrinkly. Fortunately exessive points are easily removed without deleting a part of the curve, too and the curve is easily dragged to its place with the editing tool. Changing the control point type for example from smooth to sharp is nicely behind the left click.
ADDENDUM: How to draw the shapes without a need to drag handles as you draw
If you feel it difficult to draw Bezier curves to their final forms on the fly, you can as well make at first line segments. Simply click with the pen tool to corner points and on the middle points of long curves:
Take the curve editing tool and right-click a line segment. Select "To curve" from the context menu. Then drag the curve to its final place. Do not touch the control handles, they will adapt automatically as you drag. This took less than 5 seconds:
Do the same to all line segments:
This method is good because dragging the handles on the fly entrap into inserting unnecessary control points. This way it's easier to stay diciplined.
You may need to add a control point where the curvature changes too steeply. It needs only a double-click on the curve. An unnecessary control point can be selected by clicking it and deleted by pressing DEL.
ADD2: Just for curiosity I checked, how to do this shape in 3D. Very soon appeared that Illustrators 3D effects used in trivial ways are not enough. Some underhood knowledge or an ability to see something non-obvious is needed. My results = nothing even distantly resembling from Illustrator's 3D
A little resembling 3D model come out from DesignSpark Mechanical (a simplified, but free 3D solid modelled). Photoshop had usable colors and lights to render it with shades.It's here as PS screenshot:
Geometrically this is not ok because it's made by subtracting a twisted plane from a thin sphere. There was no easy way to define the right subtracted part. The subtracted stripe is far too wide near the poles.
The following is not better:
The subtracted stripe gets too narrow towards the poles. To solve the problem the part dimensions should be calculated much before seeing the result. Another way would be to have a parametric CAD program to be able to play with starting parameters for the right visual final appearance. This ability is not available as freeware.