1) Would it be fine if I create a PR to SciPy's codebase to adopt pocketfft? The PR could give me an understanding of how to contribute to SciPy's fftpack module.
I would prefer to wait a little bit with that. The branching of 1.16.x in the NumPy repo is imminent (1-3 weeks I expect), and at that point Pocketfft can be merged into NumPy. Then we'll be able to have a discussion with the author, and port things to SciPy. I think having two PRs for Pocketfft integration going on in parallel is a bit much and likely will lead to duplicate work.