Is buying a house with a loan from a state-affiliated social institution, with low interest and specific conditions (such as not owning another property, having a low income, not selling before 8 years, living in it and not renting it out or converting it into a commercial premise, and not buying a second house), permissible, or does it fall under the category of usury, knowing that the state refunds a large percentage of the interest?

A loan with interest is usury, which is forbidden and is considered one of the major sins. Its prohibition is absolute and does not depend on whether the interest is small or large. Your taking out this loan is forbidden and necessitates repentance and prompt repayment. Your purchase and ownership of the house are valid; the problem lies in the usurious loan, not in the sale. Therefore, there is no sin upon you in keeping the house. The sin lies in the continuation of the usurious loan, so you should hasten to repay it.