Automate npm publication as @node-core/doc-kit with version bump workflow

[ovflowd]

Enter your suggestions in details:

Goal: Publish the doc-kit package on npm as @node-core/doc-kit.

Automation: Use a similar workflow for automatically publishing the package on a new version bump as implemented for @node-core/ui-components in the @nodejs/nodejs.org repository.

Details:

• Automate the npm publish process so that every time a new version of @node-core/doc-kit is released, it is automatically published to npm.
• Use GitHub Actions to implement this automation, leveraging the workflow already established for @node-core/ui-components in @nodejs/nodejs.org as a reference.
• The publish.mjs script in ui-components generates a cleaned package.json in dist/, copies documentation, and runs pnpm publish --no-git-checks in the dist directory.
• The workflow is set up so publishing is triggered on merges to main (after CI success) or via workflow_dispatch. More info and diagrams: docs/package-publishing.md.
• The monorepo structure supports independent package publishing managed by GitHub Actions.
• Document any secrets (npm tokens), configuration steps, or permission requirements for publishing—including any changes needed for branch protection, secrets, or CI.

Plan:

1. Review ui-components publish script and docs.
2. Adapt a similar workflow and script for use in doc-kit (ensure it strips devDependencies, formats paths, and publishes from dist/).
3. Create a GitHub Action to trigger the publish job after a version bump, following merge to main or manual trigger—ensure it depends on the successful completion of tests.
4. Test by bumping @node-core/doc-kit version and verifying an automated npm publish.
5. Document the setup and maintenance steps in the repository README.

References:

• publish.mjs script for ui-components
• Publishing process documentation
• Example mermaid workflow diagram in docs

[avivkeller]

I believe we should do @nodejs/doc-kit, since this tool is meant to (eventually) be used outside just node core.

(I can start working on this)

[avivkeller]

(I did not mean to assign copilot 😅)