WooCommerce Block Checkout Example to listen for payment method change and add a fee server side

test-plugin.php

<?php

// Reset payment method in session
add_action('woocommerce_checkout_init', function(){
	if( ( defined( 'REST_REQUEST' ) && REST_REQUEST ) || ( defined( 'DOING_AJAX') && DOING_AJAX ) || !WC() || !WC()->session || is_admin() ) {
		return;
	}

	// Get first payment method and store it
	// Since payment method selection is not persistent, on page load always the first one will be selected
	$available_gateways = WC()->payment_gateways->get_available_payment_gateways();
	$first_payment_method = key($available_gateways);
	WC()->session->set('test_plugin_selected_payment_method', $first_payment_method);
});

// Update callback to store the posted payment method for later usage.
add_action( 'woocommerce_blocks_loaded', function() {
	woocommerce_store_api_register_update_callback([
		'namespace' => 'test-plugin-namespace',
		'callback'  => function( $data ) {
			if ( isset( $data['payment_method'] ) ) {
				WC()->session->set('test_plugin_selected_payment_method', $data['payment_method']);
			}
		}
	]);
});

// Add fee logic.
add_action( 'woocommerce_cart_calculate_fees', function() {
	$chosen_payment_method_id = WC()->session->get('test_plugin_selected_payment_method');

	if ( 'bacs' === $chosen_payment_method_id ) {
		WC()->cart->add_fee( 'Additional Fee', 10 );
	}
});

// Move to dedicated script. Used here as quick example.
add_action( 'wp_footer', function() {
	?>
	<script>
		document.addEventListener("DOMContentLoaded", function() {
			wp.hooks.addAction(
				// This is the action hook.
				'experimental__woocommerce_blocks-checkout-set-active-payment-method',
				// This is your unique plugin namespace.
				'test-plugin-namespace',
				function( payment_method ) {
					// Log to console to demonstrate it working.
					console.log(payment_method);
					// Trigger API call.
					window.wc.blocksCheckout.extensionCartUpdate( {
						namespace: 'test-plugin-namespace',
						data: {
							payment_method: payment_method.value
						}
					} );
				}
			);
		});
	</script>
	<?php
});

Subscribing to the wc/store/payment is better than set-active-payment-method because it's also called on mount.

Weirdly, the set-active-payment-method filter would give different payload depending if you selected a regular payment method (value) or a saved payment method paymentMethodSlug.