alternative for ArcGIS command "Spatial Join" in FME?

You can try the Clipper: if the Clipper feature is a solid and the Clippee is a point cloud it should work.

You could resolve it by testing with NeighborFinder in the X-Y plane, and in parallel test with another NeighborFinder in the X-Z plane. This is essentially how 3D spatial comparisons are made in equivalent GIS tools.

To do the second NeighborFinder in the X-Z plane, overwrite the existing Y value with a VertexCreator to replace it with the Z values since NeighbourFinder only looks at the X and Y values, so you'll need to substitute the Z value into the Y coordinate to use it on the X-Z plane.

Then a FeatureJoiner between the two NeighborFinder results will give the Pairs of Points that are within distance D in both the X-Y and X-Z planes. This is the nearest points within a 3D box with a side length = 2 x D.

Then it is just a final Tester on the pairs of Points within this box to check spherical distance to see if the Candidate Points are within Pythagorean distance L = √(Delta x2 + Delta y2 + Delta z2) to the Test Point. Again, this is just replicating what steps the all-in-one ArcTool like Spatial Join does in 2D/3D.