> So the spherical harmonic functions are also the shape of the various electron orbitals that you see in a chemistry textbook.

Minor nitpick: Chemistry textbooks usually use the “cubic harmonics” instead of the “spherical harmonics”. They are real-valued linear combinations of the standard spherical harmonics, with the additional benefit that the basis set respects the Cartesian symmetries.

For example, the “p_z orbital” is a l=1 spherical harmonic and a cubic harmonic. But the cubic harmonics then add p_x and p_y orbitals as basis functions, whereas the spherical harmonics choose the chiral "p_x ± ip_y orbitals” as its basis instead.