What is the position of teachers who take teaching as a profession and receive wages for it, in relation to the reward mentioned in the hadiths that speak of the virtue of those who teach people beneficial knowledge?

The knowledge encouraged by Islam includes every beneficial science, whether it is religious or worldly, such as medicine and engineering. All of these benefit humanity and contribute to the development of the earth. The sciences of Sharia (definition) have a special status due to their connection with Allah. It is not permissible to learn the sciences of Sharia for the sake of money or prestige. As for worldly sciences, there is no objection to seeking them to obtain a job or money, and purifying one's intention therein for Allah increases the reward of its pursuer.