[actions] Fix Cygwin workflow HOME variable to resolve nvm installation path issues

[Copilot]

Problem

The Cygwin workflow in .github/workflows/windows-npm.yml was failing because $HOME/.nvm/nvm.sh does not exist after running the install script under Cygwin. This is due to an upstream change in GitHub Actions or Cygwin's handling of the $HOME variable, causing nvm to be installed in a different location than expected.

The workflow was encountering:

• File not found errors when trying to source $HOME/.nvm/nvm.sh
• nvm: command not found errors in subsequent commands

Solution

This PR fixes the issue by ensuring nvm is installed and sourced from the correct path in the Cygwin environment:

1. Set HOME explicitly: Added export HOME="$(cygpath -u "$USERPROFILE")" to set the HOME variable to the Windows user directory using Cygwin's cygpath utility
2. Added debug output: Added echo "HOME is $HOME" to verify the HOME location is correct
3. Added verification: Added ls -l $HOME/.nvm to confirm the nvm directory exists in the expected location

Changes Made

cat >~/setup.sh <<EOM
  unset npm_config_prefix
  export NVM_INSTALL_GITHUB_REPO="$NVM_INSTALL_GITHUB_REPO"
  export NVM_INSTALL_VERSION="$NVM_INSTALL_VERSION"
+ export HOME="$(cygpath -u "$USERPROFILE")"

+ echo "HOME is $HOME"
  curl -fsSLo- "https://raw.githubusercontent.com/${NVM_INSTALL_GITHUB_REPO}/${NVM_INSTALL_VERSION}/install.sh" | bash
+ ls -l $HOME/.nvm
  . "$HOME/.nvm/nvm.sh"
  nvm install --lts

These minimal changes ensure that:

• The $HOME variable points to the correct Windows user directory in Cygwin
• nvm is installed in the expected location ($HOME/.nvm/)
• The workflow can successfully source nvm.sh and execute nvm commands
• Debug output helps verify the installation path is correct

This resolves the file not found and nvm: command not found errors under Cygwin on GitHub Actions.

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