Is the funeral prayer given precedence over the Sunnah of Dhuhr based on the priority of the obligatory over the supererogatory and the Hadith "Three things are not to be delayed"?

If there is a concern that the funeral prayer might be missed, then it takes precedence over the Sunnah (supererogatory) prayer of Dhuhr, and the Sunnah prayer is performed afterwards. However, if there is no such concern, one should pray the Sunnah of Dhuhr first, then the funeral prayer, as the two rak'ahs of Sunnah are not considered a delay for the funeral prayer. A hadith states: "O Ali, do not delay three things: prayer when its time is due, a funeral when it is present, and a single woman when a suitable match is found for her." This is supported by authentic hadiths regarding hastening the funeral.