RTL, the Luxemburgish media which has access to the best information from the court, writes that it was a "Messe d'action de grâce pour le baptême de SAR le Prince Charles avec les rites complémentaires du baptême". French is my native language and in French, "rites complémentaires du baptême" refer to the anointing, the giving of the candle and the white garnment. It nevers refers to the gesture with water. I have looked at every pic the medias have published : not a single one is showing little Charles receving water on his forehead. Not a single one. However, there are plenty of pics with the anointing, the white garnment and the candle. Here are some with the candle.
https://www.wort.lu/de/politik/die-taufe-von-prinz-charles-5f6596e8de135b92363fcf63
Usually, the date on the candle is the baptism date. On this pic, the date on the candle is his birth date. As we know HGD had an emergency C-section, my hypothesis is that there was some fear for his life or his health at birth, which have quickly disappeared as he was said to do well in the birth announcement. However, I stand with my take : he was not christened today but earlier. I thought on why the medias and the court used to word "baptism" : that was Charles's big day, a feast around him. Usually, when there is an
ondoiement, as we say in French, there is a traditional feast, the same for any other baptism, the day the complementary rites are performed. A friend knew this for one of her sons.