Does one who dies after performing Hajj, but without having offered a sacrifice, incur sin, and what is the expiation for that, if any?

The Udhiyah (definition) (sacrifice) is a Sunnah (definition) and not obligatory according to the majority of scholars, and this is the most preponderant opinion. There is no sin upon whoever leaves it, and they are not required to make up for it nor offer expiation for leaving it. As for the Hady (sacrificial animal) for Tamattu' and Qiran (definition) (types of Hajj), it is obligatory. If it is not slaughtered at its appointed time (the Day of Sacrifice and the days of Tashreeq), then it must be made up for and slaughtered in Makkah or Mina because it is a debt firmly established upon one's responsibility.