How can one pay Zakat on money deposited in a bank, the interest from which is relied upon to cover essential expenses such as children's education and household necessities, especially if paying the full Zakat would reduce this interest and increase their financial burdens given the difficult economic circumstances?

You must withdraw the money from the usurious bank and repent to Allah, and invest the money in Islamic banks or permissible investment avenues, because dealing with usurious banks and depositing money in them is prohibited. The interest taken from these banks is usury, which must be disposed of by spending it on Muslim welfare or charitable organizations. Zakat (definition) is obligatory on the principal amount only if it reaches the nisab (definition) and a full year has passed over it, and it is not waived due to high prices. Zakat must be paid in full without hesitation or reduction, as the poor and needy are most in need of it during times of high prices.