Is it permissible to take a loan from an Islamic bank that finances small projects by purchasing supplies and goods for the project and then repaying the amount in installments with an added profit margin, or does this fall under the category of usury (riba)?

If the bank buys the goods and sells them to you at a profit after possessing them, this is a permissible murabaha, provided that there is no prior agreement between you and the original seller concerning them. The bank is the one that buys them first and then sells them to you. It is not permissible for you to buy the goods and for the bank to undertake paying the price on your behalf with an increase, because this is an interest-based loan.