Is taking an additional amount from the buyer for myself, outside the invoice agreed upon with the company, considered unlawful gain (haram), or should it be added to the invoice as a price increase, or should it be rejected entirely?

This increase is not permissible to take except with the company's permission, because its ruling is the same as the gifts to workers that are forbidden in the authentic hadiths. In Sahih (definition) al-Bukhari and Sahih Muslim, the Prophet, peace and blessings be upon him, said about the worker who says: "This is for you, and this was gifted to me": "Why did he not stay in his father’s house or his mother’s house to see whether he would be gifted anything or not?! By the One in whose hand is Muhammad’s soul, none of you takes anything from it except that he will come with it on the Day of Resurrection, carrying it on his neck."