How to have same users in multiple web apps and simple php pages?

I am trying to make a project that has a Magento-based Store, a Wordpress-based blog and also a simple php-based site I made myself. All of the sites have the same domain( i.e. the Magento store is domain.com/store and the blog is domain.com/blog etc.)

I am looking for a way to add the following functionality:

1. If a user signs up on one app, it also signs up on the rest.
2. If a user signs in on one app, the login stays on the other too.
3. The different apps stay separate such that any app can easily be taken out and replaced or new services added.
4. In case I add a new service, I want to make it so that the new service can access all the users previously added as well.

To clarify a little, this means that the users also have the same credentials across all apps.

I have seen and read many topics like this one or this one but they're not really answering my question.

I'm thinking that I need a separate service that authenticates the users for all apps externally. However, I am unsure how to do that, especially with the site I made. I can probably find plug-ins for stuff like Wordpress and Magento but need some guidance with doing the same using simple php.

Any resources and suggestions are greatly appreciated.