Is praying four rak'ahs after Dhuhr considered a supererogatory prayer, and is it connected to the hadith: "May Allah have mercy on a person who prays four rak'ahs before Asr"?

Praying four rak'ahs before Dhuhr and four after it is recommended and encouraged, based on the Prophet's (peace be upon him) saying: "Whoever prays four (rak'ahs) before Dhuhr and four after it, Allah will forbid him from the Fire." To maintain this virtue, one must persevere in performing them.

Similarly, the encouragement to pray four rak'ahs before Asr has been established, based on his (peace be upon him) saying: "May Allah have mercy on a person who prays four (rak'ahs) before Asr."