Magento doesn't do what you're looking for which is Single Sign on, out of the box. WHen a customer logs in, Magento sets a session cookie for the current domain. For the most part, browsers only allow you to set a cookie for the current domain as a security feature. That means when you go to the other domain, the cookie is not present, and the customer is not logged in.
The share customer feature is just a backend feature to mean that the customer could log in to any of the websites but not that they stay logged in when moving between domains.
That is a lot more tricky to perform. I don't have any suggestions off the top of my head for that. You'd need to look into how single-sign-on systems are built in general and then replicate that.
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