Your reference video illustrates a way of applying 3D decals to curved surfaces, filleting and concealing the junctions between the decals and the surface.
The way I went with your example involved quite a bit of incremental adjustment - I'll just try to cover the main points:
- Sanitize the mesh. Your decal had a lot of duplicate faces and vertices, normals pointing the wrong way.. possibly from abandoned extrusions / solidifies? To locate errors, H hide some faces in Edit Mode to check for duplicate or internal faces, jiggle some vertices around.. Use Overlays in the 3D view to display normals, face orientation. Delete surplus faces and AltM merge vertices by distance to leave yourself with a single skin.
- Consider the method. The reference method is well-suited to small decals, in the scale of the curvature of the substrate...
...asking the Shrinkwrap modifier to cover the gap at the extremes, here, is pushing it. The parts of the decal which you'd like to spread on the surface will wind up piled on top of one another. Fixes for this might be to model the decal with a curvature more similar to the substrate, or 'pre-bend' the whole decal with a Lattice modifier, (the lattice shrink-wrapped to the surface) before assigning the other modifiers... but I guess that's what the reference was trying to avoid.
The decal in the reference is modeled with a skirt, part of which will conform to the surface closely,and become the fillet after deformation, so I added one to yours.
- Adapt the method I found that with such a large decal, 2 vertex groups helped. One to deform the mesh with the shrink-wrap..
and a smaller one to pick up the normals from the sphere...
The vertex-groups can be edited 'live', under the influence of the modifiers by assigning edge-loops with weights in the decal's Data > Vertex Groups panel, so you can see what they are doing.
This result is sort of getting there..
.. but I think things would be easier if you bent the decal as a whole, preparatory to making the invisible fillet.