So, this is the same thing I am already explaining in the other thread, but Cycles doesn’t really have the option to turn off world shadows.
The easiest way to have no world shadows is to render in Eevee.
If you need Cycles, you can get a somewhat similar effect by removing the diffuse component of the world material and instead use ambient occlusion in add mode (so it adds light). There is an option for AO in the render settings, but it’s limited in what it can do. For better control, you can instead add it in the materials of your objects by using an add shader:
An other option instead of using ambient occlusion would be to replace the diffuse component of the world with a flat color rather than removing it. (see the world material graph I posted in my response to the other post). The world light would technically still have a shadow, but it would be blurred and would no longer have a defined edge. This method will give results similar to AO, because AO is actually an approximation of a flat sky light like this.
Finally, if you are looking to go full cartoonish, you can use the same material setup in the picture, but replace the AO node with an emissive shader with low strength. This will add a slight, flat color to everything and will result in a flattened, 2D animation like look.
A little word about ambient occlusion:
Modern renderers like Cycles tend not to have an easy option for ambient occlusion, because outside of realtime renders, it’s considered to be an outdated feature, a crude approximation of sky light. By default, a flat sky color in Cycles is already producing what AO is trying to do, but in a more advanced and realistic way.