Newton: Photon falling from h meters increase its energy.

Under Newton, a photon has gravitational mass m, for which it's affected
by gravity.
1) A photon with energy E, falling under gravity effects from height h,
increases its energy by an amount
ΔE = +mgh
Using the equivalence m = E/c^2, its energy when it reaches ground is E
+ ΔE:
E + ΔE = E (1 + gh/c^2)
Using Planck's equivalence E = hf, it gives
f + Δf = f (1 + gh/c^2)
Then, under Newton, the frequency change is
Δf/f = +gh/c^2
The frequency of the photon increase by falling, and is blue-shifted.
On the other way around, if a photon is escaping from ground, at an
height h its frequency has decreased by
Δf/f = -gh/c^2 (red-shifted)
******************************************************
No relativity here. Only requires to accept the existence of
gravitational mass and a given equivalence mass-energy.
Von Soldner worked around this by 1801, with the deflection of light by
gravity. It took Planck to appear 100 years later to relate energy and
frequency, plus Poincaré's equivalence mass-energy  that appeared on the
recoil of his "light cannon" around 1898.
Where is relativity left after this?