“Internal Server Error” with wp_update_post

Actually, there are 2 issues in your code:

1. You were using PHP custom file name instead of menu_slug.
2. You were not using action and method attributes of form tag. When you were submitting form WordPress redirecting into admin.php?on=Turn+Registration+On which is not a valid page.

add_submenu_page function 4th parameter must be unique menu slug of your plugin not the custom PHP file.

Please have a look at the add_submenu_page function.

I have updated the code and tested. it working fine.

add_action( 'admin_menu', 'my_admin_menu' );

function my_admin_menu() {
    add_menu_page( 'Registration Switch', 'Registration', 'manage_options', 'page-toggle', 'registration_admin_page', 'dashicons-welcome-write-blog', 6  );
}

function registration_admin_page() {
    ?>
    <div class="wrap">
        <h2>Registration Information</h2>
        <h2>Toggle Registration</h2>
        <form action="<?php echo admin_url('admin.php?page=page-toggle'); ?>" method="post">
            <input type="submit" name="on" value="Turn Registration On" class="button-secondary" onclick="return confirm('Are you sure you want to enable registration?')" />
            <br>
            <br>
            <input type="submit" name="off" value="Turn Registration Off" class="button-secondary" onclick="return confirm('Are you sure you want to disable registration?')" />
        </form>
        <?php

        if( isset( $_REQUEST['off'] )) {
          $my_post3 = array('ID' => 90,'post_status' => 'draft');
          wp_update_post( $my_post3 );
          $my_post4 = array('ID' => 83,'post_status' => 'publish');
          wp_update_post( $my_post4 );
          echo "<h2>Registration is turned OFF.</h2>";
        } elseif (isset( $_REQUEST['on'] )) {
          $my_post1 = array('ID' => 90,'post_status' => 'publish');
          wp_update_post( $my_post1 );
          $my_post2 = array('ID' => 83,'post_status' => 'draft');
          wp_update_post( $my_post2 );
          echo "<h2>Registration is turned ON.</h2>>";
        }
        ?>
    </div>
    <?php
}
?>