Save all the post tags inside a custom field

To start, why do you want to have your tag data in tags and also in a custom field? Seems to me like there is no reason for this, but maybe I’m missing something.

To answer your question about the code you have.. inside your foreach you overwrite the value each time in the loop. Instead of overwriting, you should add new tags to your predefined variable. Try this:

$all_post_tags = get_the_tags();
$count = 0;
$comma_sep = ', ';

if ( $all_post_tags && !empty($all_post_tags) ) {

    $get_all_tags="";

    foreach ( $all_post_tags as $tag ) {
        $get_all_tags .= $tag->name . $comma_sep;
    }

    add_post_meta($post->ID, 'all_tags', $get_all_tags, true);

}