Hat tip to @[email protected] who gave me the answer on Mastodon.

buildNpmPackage inherits from mkDerivation, so you can just get the directory by overriding postInstall.

buildNpmPackage rec {
  npmDepsHash = "sha256-+4lLBQ+UQ2XT0wwE6jADxG1UNZjLkQCLvvN1SdiUwZY=";
  pname = "mysite";
  src = fs.toSource {
    root = ./.;
    fileset = sourceFiles;
  };
  postInstall = ''
cp -rv public/ $out
'';
  version = "0.0.1";