What is the ruling on taking back one's capital along with an equivalent amount as a loan from one of the partners in exchange for withdrawing from the project? Is that considered usury (riba)?

If you wish to exit the company, it is permissible to sell your share to one of the partners or to a third party at the agreed-upon price.

However, the scenario mentioned in the question (combining sale and loan) is not permissible, due to the Prophet's (peace be upon him) prohibition of it, as he said: "It is not lawful to combine a loan and a sale." This is because it is a means to usury (riba), as the price enters into the realm of uncertainty, or the loan is conditioned upon a benefit, and every loan that brings a benefit is usury.