Display users by role

Question

What I understand from your code: You want to list users with author role.

You’re in the right direction, however, following are some tips to make your code better.

Use role id in lowercase syntax. Change Author to author for role property.
Get the results for once and avoid repeated calls. Save the results like $authors = $user_query->get_the_results(); then, use if (!empty($authors)) { ... } to check and foreach($authors as $author) {...} to loop through.
Wrap the actual results in <ol> or <ul> or other needed element, so, start the <ol> tag only if results are found and close the </ol> tag right after foreach loop. For the else content, use other HTML element such as <p> with a error code style class etc.
Consider pagination for high number of users. Consider the case when the total matched users go up to 100+ to 1000s over the time.

After applying the given tips, the code is as follows: –

Without pagination

<?php
$args = array(
    'role'    => 'author', // changed Author to author
    'orderby' => 'user_nicename',
    'order'   => 'ASC'
);
$authors_query = new WP_User_Query($args); // enhanced the variable name from $user_query to $authors_query 
$authors = $authors_query->get_results(); // saved the results for once to avoid repeated calls later on
?>

<?php if (!empty($authors)) { ?>
    <table> <!-- Replaced ol to table element -->
        <thead>
            <th>Name</th>
            <th>Details</th>
            <th>URL</th>
        </thead>
        <?php foreach ($authors as $user ) { ?>
            <tr>
                <td><?php echo $user->display_name ?></td>
                <td>
                    <?php echo $user->ID ?> | <?php echo $user->user_login ?> | <?php echo $user->user_email ?> 
                </td>
                <td><?php echo $user->user_url ?></td>
            </tr>
        <?php } //endforeach ?>
        </table>
<?php } else { ?>
    <p class="no-results-notice">No authors found.</p>
<?php } ?>

With pagination

<?php

//Pagination
$page = isset($_GET['show_authors']) ? $_GET['show_authors'] : 1;
$authors_per_page = 20;  // you can change the number as needed
$total_pages = 1; // initial value; keep it one; we will update this after having actual number of users from query
$offset = $authors_per_page * ($page - 1);


$args = array(
    'role'    => 'author', // changed Author to author
    'orderby' => 'user_nicename',
    'order'   => 'ASC'
);
$authors_query = new WP_User_Query($args); // enhanced the variable name from $user_query to $authors_query 
$authors = $authors_query->get_results(); // saved the results for once to avoid repeated calls later on

// Updating variables for pagination.
$total_authors = $authors_query->get_total(); 
$total_pages = ceil($total_authors / $authors_per_page); 

?>

<?php if (!empty($authors)) { ?>
    <h2>We have <?php echo $total_authors; ?> authors in our website. </h2>
    <table> <!-- Replaced ol to table element -->
        <thead>
            <th>Name</th>
            <th>Details</th>
            <th>URL</th>
        </thead>
        <?php foreach ($authors as $user ) { ?>
            <tr>
                <td><?php echo $user->display_name ?></td>
                <td>
                    <?php echo $user->ID ?> | <?php echo $user->user_login ?> | <?php echo $user->user_email ?> 
                </td>
                <td><?php echo $user->user_url ?></td>
            </tr>
        <?php } //endforeach ?>
        </table>

        <!-- Display Pagination Links -->
        <div class="authors-pagination">
            <?php                 
                echo paginate_links( array(
                    'base'         => add_query_arg( 'show_authors', '%#%' ) ,
                    'total'        => $total_pages,
                    'current'      => $page,
                    'format'       => '',
                    'type'         => 'plain',
                    'end_size'     => 1,
                    'mid_size'     => 1,
                    'prev_next'    => true,
                    'prev_text'    => sprintf( '<i></i> %1$s', __( 'Previous', 'text-domain' ) ),
                    'next_text'    => sprintf( '%1$s <i></i>', __( 'Next', 'text-domain' ) )
                ) );
            ?>
        </div>

<?php } else { ?>
    <p class="no-results-notice">No authors found.</p>
<?php } ?>

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