Make package-manager detection always consult `npm_config_user_agent` before looking for lockfiles or probing installed executables. A recognized invoking package manager must win even when a project has a conflicting lockfile, so an npm-driven invocation inside a pnpm or yarn project is detected as npm rather than inferred from the project.

Use the consistent user-agent order yarn, pnpm, bun, then npm across the package-manager detection used by Next.js, `@next/codemod`, and `create-next-app`. `create-next-app` already behaves this way and should remain unchanged. The Next.js helper's `PackageManager` type has no bun, so a bun user agent there must fall through to its existing lockfile and fallback detection.

For codemod lockfile discovery, use the corresponding precedence `yarn.lock`, `pnpm-lock.yaml`, `bun.lock`/`bun.lockb`, then `package-lock.json` when multiple candidates are present. Preserve existing fallback behavior when the user agent is absent or unrecognized, and return immediately for a recognized user agent so filesystem and subprocess fallback work is avoided.