Best Of

The majority of 3D artists make this mistake. A lot can be said for what kind of geometry to use in this situation, but the fundamental problem is straightforward:

You fell for the temptation to simply extrude the quads straight off of the cylinder. As a consequence, your transition geometry (the part going from cylinder to box) is the size of one of the segments of the cylinder. If you simply offset the extrusion you can hide the transition shading errors in smaller geometry.

In sub-division modeling you are bound to get shading errors. That's sub-d. The trick is knowing where to place them.

Left: Transition geometry is large polygons

Right: Transition geometry is small polygons

They both have shading errors, but the ones on the right are less visible simply because they are smaller,

When people do not understand this principle, they end up adding an unmanageable amount of sements to their cylinder (or whatever shape), which technically works because it has the effect of limiting the affected area. Here the area is limited without adding segments, It is exactly the same add adding a ton of segments, without adding a ton of segments.

its very rare that being 100% dogmatic is the best approach

your uvs want to look something like this (but not crudely drawn with a mouse while eating soup)

While it's fine to learn about doing stuff properly, keep in mind this kind of artefact might be invisible in the final asset with all the texturing work/texture resolution/viewer distance... So don't waste too much energy trying to be perfect while it could be used for more useful details.

By it's own nature, subd can't be perfect, you just reduce the scale of artefacts to the point where no one can notice.