I understood what you said. No need to show screenshots.
If you can access your database via PHPMyAdmin in your host, then take a look in the core_tags table. That's the table my app uses. There's also the core_tags_cache, which stores the tags/prefix used in the items. Both tables are tied to each other: core_tags.tag_aai_lookup = core_tags_cache.tag_cache_key.
That's the query to get the counter:
$rows = array();
foreach( \IPS\Db::i()->select( 'tag_text, count(tag_text) as cnt, SUM(tag_prefix) as prefixed, MAX(tag_added) as last', 'core_tags', array( 'tag_meta_app=?', \IPS\Request::i()->fromApp ), $order, null, 'tag_text' ) as $row )
{
$rows[] = $row;
}
I don't use the cache anywhere, which means it is controlled by Core somehow.
EDIT: your image also shows it is still in use. Provide an ACP account and URL and I'll take a look directly in your database.