What is the ruling on going for Umrah while having a debt to the bank, knowing that it is obligatory to settle debts before Hajj or Umrah?

If the loan is interest-based (usurious), it is forbidden and a major sin. One must repent to Allah for it. However, if it is an interest-free loan (qard hasan (definition)), then it is permissible.

Regarding Hajj, the preponderant opinion is that repaying debt takes precedence over Hajj, because Hajj is not obligatory for a debtor who is unable to pay. If Hajj does not conflict with debt repayment (for example, if the repayment date is delayed or the creditor is patient), then performing Hajj is permissible. For Hajj, complete ability is a condition, which includes repaying due debts and providing for one's dependents and those whose maintenance is obligatory.