We dropped Cygwin support in September 2022,
https://github.com/sagemath/sage/wiki/Sage-9.7-Release-Tour
but that was mainly a documentation change reflecting the fact that
Cygwin support had bit-rotted.
Anyone could have fixed it at that point -- or in the meantime -- but
no one has done so. I think it's time to admit that Cygwin is a dead
platform for us. WSL is a much easier replacement these days if your
goal is to get Sage running on Windows.
The issue was made relevant again by PR #36129 which reintroduces the
psutil package as standard. The meat of psutil is platform-specific C
code that does not work on Cygwin, and it's not something we can
realistically fix.
If it's never coming back, I'd like to start removing the old Cygwin
workarounds from sage. This is your heads up in case there are still
users out there.