Is it permissible for a partner to obtain a hidden additional profit by purchasing project supplies at reduced prices and selling them to the project at market price, and is the other partner required to be informed of this?

Since the company is built on agency and trust, it is not permissible to take a commission on the purchase of medicines, fodder, or anything else without the partner's permission and knowledge. One must repent to Allah for transgressing against the company's funds by returning any commissions taken unlawfully, or by informing the partner and seeking their forgiveness. If they forgive you, then there is nothing upon you; otherwise, the right must be returned to the company.