Adding register & login at top right corner

Question

UPDATED:
In the header.php you have these lines:

     </div><!-- .hm-site-title -->
</div><!-- .site-branding-content -->

You’ll want to put your div tag for the register and login buttons between them:

</div><!-- .hm-site-title -->
    <div class="hm-custom-login-btns">
        <?php
        $c_user = wp_get_current_user();
        if( !is_user_logged_in( $c_user->ID ) ) :
        echo '<a href="' . esc_url( wp_login_url() ) . '" alt="' . esc_attr_e( 'Login', 'textdomain' ) . '">';
            echo _e( 'Login', 'textdomain' );
        echo '</a>';
        wp_register('', '');
        else :
            echo 'Hello ' . $c_user->display_name;
        endif;
        ?>
    </div>
</div><!-- .site-branding-content -->

Then you’ll need to work with CSS to get it all positioned correctly. You’ll probably need to adjust the container widths, and either float elements left and right or use display:flex and associated properties to lay it all out.

The Login & Register link generating PHP can be found here:
https://developer.wordpress.org/reference/functions/wp_login_url/

https://developer.wordpress.org/reference/functions/wp_register/

And here’s how you obtain the user’s display name and other info:
https://developer.wordpress.org/reference/functions/wp_get_current_user/