mashallah nice explanation some of the things which i could add
Wudu or ablution may be performed for any purpose, and praying 2 rakaats after every wudu as 'tahiyyat-al wazu' is a highly meritorious act. Aqaba Ibn Amir has related that the blessed Prophet said, "When one performs ablution and performs it well and then prays 2 rakaats in such a way that his face, and also his heart are turned to Allah, Paradise becomes a certainty for him." (Muslim, Abu Da'ud, Nisai)
Abu Hurairah has related that the eternally blessed Messenger of Allah said to Bilal, "Tell me from which of your acts you expect the most merit, because during Meraj (Assention), I heard your footsteps in front of me." Bilal said, "The act due to which I expect maximum mercy from Allah is that whenever during day or night, I have performed ablution, I have prayed as much as I could." (Bukhari and Muslim)
It takes two to three minutes to pray 2 rakaats after ablution, but it is immensely rewarding. If it is time for one of the 5 compulsory prayers, then it is better to pray 2 rakaats tahiyyat-al wudu first, but if there is no time then fard or sunnah should be performed with (additional) intent of tahiyyat-al wudu. This might earn the merit due to tahiyyat-al wudu.