Issue installing python bcrypt in Cygwin

I’m trying to install paramiko in Cygwin and one of the build dependencies is bcrypt.
I have rustc installed and I believe all of the supporting build libraries.

Pip is also updated to the latest.

$ pip --version
pip 22.2.2 from /usr/local/lib/python3.8/site-packages/pip (python 3.8)

I use the following pip command:

pip install bcrypt

And I get the following error output:

  error: failed to run custom build command for `pyo3-build-config v0.15.2`

  Caused by:
    process didn't exit successfully: `C:Cygwin64tmppip-install-19d9duslbcrypt_117761e212a240d8804ceae0beeb39c1src_bcrypttargetreleasebuildpyo3-build-config-2ef06b5f5d02e46bbuild-script-build` (exit code: 1)
    --- stdout
    cargo:rerun-if-env-changed=PYO3_CONFIG_FILE
    cargo:rerun-if-env-changed=PYO3_NO_PYTHON
    cargo:rerun-if-env-changed=PYO3_PYTHON

    --- stderr
    error: failed to run the Python interpreter at /usr/bin/python.exe: The system cannot find the path specified. (os error 3)
  warning: build failed, waiting for other jobs to finish...
  cargo rustc --lib --message-format=json-render-diagnostics --manifest-path src/_bcrypt/Cargo.toml --release -v --features pyo3/abi3-py36 pyo3/extension-module -- --crate-type cdylib

      =============================DEBUG ASSISTANCE=============================
      If you are seeing a compilation error please try the following steps to
      successfully install bcrypt:
      1) Upgrade to the latest pip and try again. This will fix errors for most
         users. See: https://pip.pypa.io/en/stable/installing/#upgrading-pip
      2) Ensure you have a recent Rust toolchain installed. bcrypt requires
         rustc >= 1.56.0.

      Python: 3.8.12
      platform: CYGWIN_NT-10.0-19044-3.3.5-341.x86_64-x86_64-64bit-WindowsPE
      pip: n/a
      setuptools: 65.3.0
      setuptools_rust: 1.5.1
      rustc: 1.63.0 (4b91a6ea7 2022-08-08)
      =============================DEBUG ASSISTANCE=============================

  error: `cargo rustc --lib --message-format=json-render-diagnostics --manifest-path src/_bcrypt/Cargo.toml --release -v --features 'pyo3/abi3-py36 pyo3/extension-module' -- --crate-type cdylib` failed with code 101
  [end of output]

  note: This error originates from a subprocess, and is likely not a problem with pip.   ERROR: Failed building wheel for bcrypt Failed to build bcrypt ERROR: Could not build wheels for bcrypt, which is required to install pyproject.toml-based projects

I check my python installation (python.exe) and it is installed at /usr/bin/python.exe.

$ ls /usr/bin/python*
/usr/bin/python.exe        /usr/bin/python2.7.exe   /usr/bin/python3.8-config
/usr/bin/python2-config    /usr/bin/python3         /usr/bin/python3.8.exe
/usr/bin/python2.7-config  /usr/bin/python3-config

So I am confused…..what is the issue? Why can’t it find my python interpreter? Why is bcrypt not building and installing?