Is it permissible to bargain over legitimate financial rights and to tie their recovery to relinquishing other rights, especially after obtaining a higher academic qualification with the employer's approval?

The reference for judgment in this matter is knowledge of the laws and regulations governing work. If officials violate them to prevent the questioner from their right, then it is oppression and an abuse of authority. Otherwise, the general principle is that Muslims abide by their conditions, and that the contract is the law between the contracting parties, as long as it does not violate a Sharia (definition) ruling.