The full antenna length for a half wave dipole, is somewhat less then a half wavelength, Each pole is about 45 mm.
Your formula is to get the starting values for a so-called halve wave dipole in free air (as the length is about half of a full wave).
Dielectrics do affect the resonance frequency. The amount of length reduction depends on how much of the E-field path is through dielectric. More close: the smaller integral(E*ds)/(wire voltage), the less the influence. "s" is distance in dielectric. Same dielectric at some distance has less influence than same dielectric touching the antenna. A thin PCB will have less effect then a thick PCB. There are no closed form equations for this problem.
You will notice a huge change when there is a groundplane under your dipole as in that case virtually all field lines have to go through the dielectric. The dielectric has the effect of reducing the wave propagation speed in the dipole conductors, so the wavelength reduces.
If, due to the dielectric, the wavelength reduces from 212 to 100mm, your half wave antenna would have a length of about 45mm.
You may look into patch antenna design, there you will see that the actual patch size is mostly far below a half wave length for free space.