Is it permissible to take out an interest-bearing loan to buy an apartment, given a bitter experience with renting, insufficient savings, and failure to meet the conditions of the Islamic bank, and is this situation considered a necessity?

Usury is a major sin. It is not permissible to engage in it except when there is a dire necessity that permits committing what is otherwise forbidden, as Allah Almighty says: "But whoever is forced [by necessity], neither desiring [it] nor transgressing [its limit], there is no sin upon him. Indeed, Allah is Forgiving and Merciful." (Al-Baqarah: 173). The fatwa of the Academy of Islamic Research in Cairo states that interest on all types of loans is forbidden usury, whether little or much. The sin of borrowing with usury is only lifted if necessity calls for it, and each individual is left to their own conscience in assessing this necessity.