Thanks to some help from a member of the Woocommerce Community Slack group this helped me identify Tax Items by Label.
// Get all applied tax items
// $cart is passed via my function for the woocommerce_cart_calculate_fees add_action
$bs_tax_totals = $cart->get_tax_totals();
$bs_duty_exists = false;
// Check each tax item
foreach ( $bs_tax_totals as $bs_tax ) {
// Compare tax label (case-sensitive exact match)
if ( ‘Duty’ === $bs_tax->label ) {
$bs_duty_exists = true;
break;
}
}