Admin doesn’t have sufficient permissions to plugin’s page

According to the documentation for add_menu_page:

Note: If you’re running into the “You do not have sufficient permissions to access this page” error, then you’ve hooked too early. The hook you should use is admin_menu.

This means you need to wrap your menu creation in something like:

add_action( 'admin_menu', function() {
    add_menu_page(
        // page title
        'Page Title',
        // menu title
        'My Menu Title,
        // capability
        'some_capability,
        // menu slug
        'my-page',
        // callback function
        'do_my_page_content'
    );
});