How to add custom meta to 'pre_get_terms'?

Most likely because the query is also searching for a match against the term name/slug, as opposed to “match either term name or meta field”.

If you don’t need the search to also look for matches by term name/slug, just unset the search term early on when you apply your meta query:

add_action( 'parse_term_query', function ( $wp_term_query ) {
    $taxonomy = $wp_term_query->query_vars['taxonomy'];

    $search = $wp_term_query->query_vars['search'] ?? '';

    if ( ! $search || $taxonomy !== [ 'feedback-stats' ] ) {
        return;
    }

    unset( $wp_term_query->query_vars['search'] );

    $meta_query = [
        'relation' => 'OR',
    ];

    $search_meta_keys = [
        'access_id',
        // Add your other meta keys
    ];

    foreach ( $search_meta_keys as $key ) {
        $meta_query[] = [
            'key' => $key,
            'value' => $search,
            'compare' => 'LIKE',
        ];
    }

    $wp_term_query->query_vars['meta_query'] = $meta_query;
});

If you do indeed need the search to match either the term name or field(s), there’s a bit more work ahead of you as we’ll need to hook into the generated SQL of the meta query and create an OR search.

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