A formal complaint is usually acknowledged first and then reviewed under the service standards or complaint process that applies. You may receive updates during the review period, especially if the matter takes longer to resolve.
The complaint stage is not just a repeat of customer support. It is a more structured review, often handled with clearer process and timelines. That is why a clean factual summary helps a great deal.
If you send new details later, keep them in the same thread where possible so the file stays coherent.