How can I trigger actions manually?

You are currently using an anonymous function. The first step would be changing it to a named function so you can retrieve it from the wp_filter global array, which holds all the registered actions and filters. You’d do it like this:

function payment_test($form, $entry_id){
 if ( function_exists( 'gf_webhooks' ) ) {
    $entry = GFAPI::get_entry( $entry_id );
    gf_webhooks()->maybe_process_feed( $entry, $form );
    gf_feed_processor()->save()->dispatch();
  }
}
add_action( 'gform_post_payment_completed', 'payment_test', 10, 2 );

// Call it manually by getting the callable from the wp_filter global.

global $wp_filter;

call_user_func_array(
  $wp_filter['gform_post_payment_completed']->callbacks[10]['payment_test']['function'],
  $args // You have to manually provide the arguments as an array.
);