Is what I do — profiting from the plumber's wage that I arrange for the employer without his knowledge — considered unlawful (haram) or lawful (halal)?

You are not permitted to take the difference in price for yourself without the knowledge of the employer if you are his agent. The employer must be informed of the worker's true wage, and you may request a fee from him for supervising the plumber's work. The solution is to inform the employer of the difference you are taking in exchange for bringing in workers, or to agree with him that you will undertake the work for a known wage, and then you hire the workers.