For custom configurable properties, there is now the \Drupal\search_api\Processor\ConfigurablePropertyInterface::setConfiguration() which is used to set the configuration directly on the property, in case it is associated with a specific field. This can be used in methods that do not receive a \Drupal\search_api\Item\FieldInterface object as a parameter to still access the property’s configuration. (It will not necessarily be present, though, so implementers should not rely on this.)
For an example, see \Drupal\search_api\Plugin\search_api\processor\Property\AggregatedFieldProperty::isList(), which uses the new field to determine whether the property represents a list (which is the case exactly when it is set to “Union” type):
public function isList(): bool {
return ($this->configuration['type'] ?? 'union') === 'union';
}