Template Hierarchy tag-{slug}.php directory

When you look at the source code, the tag template is loaded as follow in template hierarchy

• elseif ( is_tag() && $template = get_tag_template() ) : in wp-includes/template-loader.php

• get_tag_template() uses get_query_template() which uses locate_template()

• which loads the tag template according to hierarchy from the theme root folder

So, moving your templates to a sub-folder will not work out-of-the-box. get_query_template() however have a filter (apply_filters( "{$type}_template", $template )) that we can use to change this behavior and load our tag-{$tag->slug}.php from a subfolder

So, we should do the following

• Check if our tag-{$tag->slug}.php exists in our subfolder of choice

• Load our tag-{$tag->slug}.php from subfolder if it exists

• Load default templates from the hierarchy if tag-{$tag->slug}.php does not exists in a subfolder

Something like the following will work

add_filter( 'tag_template', function ( $template )
{
    $tag = get_queried_object();
    // Alternative path to desired template
    $alternative_template = locate_template( "custom-sub-folder/tag-{$tag->slug}.php" ); // Change subfolder name

    // If we do have "tag-{$tag->slug}.php" in a subfolder, load "subfolder/tag-{$tag->slug}.php"
    if (  $alternative_template )
        return $template = $alternative_template;

    // If we don't have a "tag-{$tag->slug}.php", load templates according to hierarchy
    return $template;
});