If you are using WordPress, you need to use WP REST API.For example, you can use this solution, as you use JS,also see to the side with API solutions like this.

Considering your question is around SSO (Single Sign-On) I would point you in the direction of OAuth.

OAuth is pretty much the industry standard and means if you want to add other services such as Google, Facebook, Twitter authorization later you will be able to support these out of the box.

What would be the best solution to integrate all services (single login and password for all). LDAP / Kerberos or something else?

There are some providers that provide a SaaS platform for Authentication.Check out https://auth0.com/

They have a plan that allows you to have up to 7K free users.

WordPress

For the Wordpress piece Auth0 provide a WP plugin:https://auth0.com/wordpress

Node JS

You can use some of the SDK sample code:https://auth0.com/docs/quickstart/webapp/nodejs/01-login

Git Lab

GitLab provides an OAuth plugin:https://docs.gitlab.com/ee/integration/oauth_provider.html

Custom CLI

You could potentially write your CLI in Node JS, in that case, the above sample code should be a helpful start.

If you get stuck feel free to ask and I can point you towards some other areas as well.