What is the algorithm to generate sine waves of arbitrary frequency in the STFT domain?
The FFT of a non-integer multiple frequency is very complex, you don't want to go there!
There are various oscillator schemes that are a few MAC instructions per sample such as https://vicanek.de/articles/QuadOsc.pdf
Checkout a review here: https://www.njohnson.co.uk/pdf/drdes/Chap7.pdf