What is the ruling on taking a loan from an interest-based bank out of necessity, given the absence of Islamic financial institutions?

The transaction in question is impermissible because it involves usury (riba). It is only permissible in cases of dire necessity, where one's life or a similar unbearable hardship is at stake. If someone takes out an interest-bearing loan without necessity and establishes a project with it, their project is permissible, and its earnings are lawful. However, they must repent to Allah.