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How do I display all tags (linked) from all posts, inline, with a separator?

How do I display all tags (linked) from all posts, inline, with a separator?

I have this code but it has no separator

<?php
$tags = get_tags();
$html = '<div class="post_tags">';
foreach ( $tags as $tag ) {
    $tag_link = get_tag_link( $tag->term_id );
             
    $html .= "<a href='{$tag_link}' title='{$tag->name} Tag' class='{$tag->slug}'>";
    $html .= "{$tag->name}</a> ";
}
$html .= '</div>';
echo $html;
?>

e.g.

aaa, bbb, ccc, ddd