message appears that you are already logged in

I’m not sure I understand your question, but it sounds like maybe it could be a server-side caching issue?

It’s not a cache issue. I’m using shortecode to embed the login form on my site’s homepage. The same user already logged in to the site when entering the home page he presents the login form again, it would be right to present a message You are already logged in and the login form does not appear again. Even already logged into the site.

Here is the problem the plugin is not working as it is in the documentation. If you have an active login, you should require a panel with options and not a login form again.

Link doc:

https://docs.thememylogin.com/article/88-modifying-the-user-panel

Do notice the bold in the documentation quote:

When the widget is active with Log In selected as it’s action, a “user panel” will be shown instead of the login form.

You can add a filter to hide it when logged in:

add_filter( 'tml_shortcode', function ( $content, $action ) {
    if ( 'login' == $action && is_user_logged_in() ) {
        return '';
    }
    return $content;
}, 10, 2 );

It worked to hide the login form after login, now I need to know which shortcode to display the user panel? Because nothing appears, not even the name of the logged in user.

Use the widget.

Problem with using widget is that it is not customized and not translated into Portuguese.

How to remove Dashboard and Edit Profile links?

Another widget usage issue is invalid user password error messages or recaptch failure not working properly.

I just need you to hide login if the user is already logged in. Displays message “ALREADY LOGGED IN!”

Using the code I already provided, simply return some content instead of an empty string:

add_filter( 'tml_shortcode', function ( $content, $action ) {
    if ( 'login' == $action && is_user_logged_in() ) {
        return 'ALREADY LOGGED IN!';
    }
    return $content;
}, 10, 2 );