Bandwidth calculation of second order Sallen-Key low pass filter
is there somewhere where I am going wrong with the derivation, or is
the method of how I approach calculating bandwidth wrong?

When you calculated 662 Hz you actually calculated 662 radians per second. To convert to hertz you divide 662.134 radians per second (the precise value using your component values) by 2π to get 105.3819 Hz.
Cut-off frequency for a low pass Sallen Key filter is: -
$$F_C = \dfrac{1}{2\pi\sqrt{R_1R_2C_1C_2}}$$
Which is precisely what your algebra is telling you.