Menu Link Redirect Based on Username or User ID

I think you can make this much easier than you are. Just create a my-projects page and forget about the custom rewrite. Why? Because a user will only need to see their own projects. No need for a just rewrite because you can get the current user any time.

Embed the project rendering into a shortcode and just pop it into whatever page you want.

add_action('init', 'wpse105306_add_shortcode');
function wpse105306_add_shortcode()
{
    add_shortcode('wpse105306_projects', 'wpse105306_projects');
}

function wpse105306_projects()
{
    $user = wp_get_current_user();

    $projects = wpse105306_get_projects_somehow($user);

    // do stuff with $projects
}

function wpse105306_get_projects_somehow($user)
{
    // whatever you need here
}

That said, if you really want that url, you’ll need to do a custom rewrite.

// make the rewrite work
add_action('init', 'wpse105306_add_rewrite');
function wpse105306_add_rewrite()
{
    add_rewrite_rule(
        '^client-portal/my-projects/([^/]+)/?$',
        'index.php?wpse105306_portal=$matches[1]',
        'top'
    );
}

// make sure WordPress doesn't eat the wpse105306_portal query var
add_filter('query_vars', 'wpse105306_add_var');
function wpse105306_add_var($vars)
{
    $vars[] = 'wpse105306_portal';
    return $vars
}

Then hook in someplace late (eg. template_redirect) and if you have the query var for the portal, render the customers projects.

add_action('template_redirect', 'wpse105306_catch_portal');
function wpse105306_catch_portal()
{
    $username = get_query_var('wpse105306_portal');
    if (!$username) {
        return; // things go on as normal
    }

    $projects = wpse105306_get_projects_somehow($username);

    // do stuff with $projects
}

function wpse105306_get_projects_somehow($username)
{
    // whatever you need here
}

You might also be able to do something with add_rewrite_tag. A custom rewrite will mean you have to do some other stuff to make it work in menus. The shortcode approach above means you can use the menu system as normal.