Is it permissible for me to take a commission from a contractor in exchange for recommending him to my company, knowing that I may be part of the project's supervision team?

As long as you are commissioned by your company to find a contractor to execute the project, you are an agent for the company in this matter. An agent is not permitted to benefit personally—whether through commission or otherwise—without the knowledge of their principal. Therefore, it is not permissible for you to take a commission from the contractor, except with the permission of your company.