Is one sinful for delaying the giving of their wealth's Zakat when it becomes due, and is it permissible to delay giving Zakat until after performing the Hajj obligation?

Zakat (definition) has a known time when the (Hijri) year is complete, and it is not permissible to delay it except for a slight excuse. In your case, the period that has passed since Zakat became obligatory is long, and it appears that you had no excuse. You must repent sincerely and hasten to pay Zakat to those who are eligible. Do not prioritize anything else over absolving yourself by paying Zakat, for the obligatory is prioritized over the supererogatory. Paying Zakat takes precedence over performing the obligatory Hajj, because the right of the poor takes precedence, and because the debt owed to Allah is more deserving of being paid.