What is the algorithm to generate sine waves of arbitrary frequency in the STFT domain? I'd like to write a DSP algorithm to do additive synthesis using arbitrary sine waves with inverse rectangular FFTs.
This requires two things:

The ability to generate phase/amplitude lists that cause the IFFT to create sine waves that are not integer multiples of 1/(IFFT length)

Example:  How do I generate 1000 Hz with 16 sample IFFTs at 44100 Hz?

The ability combine two frames pre-IFFT so they are added post-fft.

What are the necessary steps here?
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