I do something similar in my energy monitor, although I tend to focus on the Current waveforms rather than the voltage. That produces pics like these.
I get 24-bit values from my ADCs at 8K SPS. When I want to look at distortion I fetch 480 of them, so about 3 cycles worth at 50Hz, and then ship them off to a “server” for FFT processing. Actually, the above pics were from an earlier version that could only do 4K SPS. The latest version does 8K.
I found some generic fft code on the interwebs to do the maths. I’ll post a pointer soon.