  The spatial structure of in-gap Yu-Shiba-Rusinov (YSR) bound states induced
by a magnetic impurity in a superconductor is the essential ingredient for the
possibility of engineering collective impurity states. Recently, a saddle-point
approximation [Phys. Rev. B 105, 144503] revealed how the spatial form of a YSR
state is controlled by an anisotropic exponential decay length, and an
anisotropic prefactor, which depends on the Fermi velocity and Fermi-surface
curvature. Here we analyze STM data on YSR states in NbSe$_2$, focusing on a
key issue that the exponential decay length predicted theoretically from the
small superconducting gap is much larger than the observed extent of YSR
states. We confirm that the exponential decay can be neglected in the analysis
of the anisotropy. Instead, we extract the anisotropic prefactor directly from
the data, matching it to the theoretical prediction, and we establish that the
theoretical expression for the prefactor alone captures the characteristic
flower-like shape of the YSR state. Surprisingly, we find that up to linear
order in the superconducting gap the anisotropic prefactor that determines the
shape of YSR states is the same as the anisotropic response to the impurity in
the underlying normal metal. Our work points out the correct way to analyze STM
data on impurities in small-gap superconductors, and reveals the importance of
the normal band structure's curvature and Fermi velocity in designing
multi-impurity in-gap states in superconductors.
