Solving d = a*exp(j*2*pi*f*t) with 256 measurements will give better accuracy than the 32k point FFT with far less computation. The sole limitation to the accuracy from computing a linear fit to the phase is the accuracy of the velocity factor and the angular accuracy of the phase measurements. A nanoVNA should be able to measure the length of an airline to 4.4 mm or less using 101 frequency magnitude and phase measurements. That's assuming a 3.6 degree phase accuracy based on a 40 dB SNR at 900 MHz.
One can do better than that by restricting the sweep to a range with higher SNR.
In summary, the number of points in the FFT is a red herring. The error cited is only an issue if the calculation is done incorrectly. One could also interpolate the sinc(t) in the time domain using 8 points to any desired sampling from a 256 point FFT. However, that would still be the wrong way to determine the delay time. Solving the equation in the first sentence is how it is properly done.
Have Fun!
Reg
