Why is blowing – whether out of boredom or to warm one’s hand – considered unlawful (haram) or disliked (makruh), and should a Muslim seek forgiveness if he blows?

If "puffing" means "sighing with annoyance," then the prohibition relates to its incompatibility with noble character and beautiful attributes. As for puffing during prayer, its ruling has been explained previously. It is unanimously disliked to blow on food and drink due to the possibility of saliva falling into it, which might disgust the drinker or eater. It also indicates haste, greed, lack of chivalry, and disrespect for food. Whoever commits a forbidden act should seek forgiveness, and there is no specific evidence for seeking forgiveness for one who blows. As for blowing on the hands for warmth outside of prayer, it is permissible.