What is the ruling on installing dental braces at the workplace clinic outside official working hours, after informing the employer and receiving no response from him, and is it permissible to deduct the cost of the treatment paid by the questioner due to the employer's delay in providing insurance from the cost of the braces if his action was unlawful?

You were not permitted to perform the orthodontic procedure in the clinic without the owner's permission, because that is considered using another's property without their willing consent, even if you bought the materials with your own money and intended to pay compensation. You must repent to Allah and restore the right to its owner or seek his forgiveness. It is best to inform him of what you did; if he forgives you, then there is nothing upon you. If he demands his right, then he is entitled to the equivalent rent. If he owes you a debt due to a delay in medical insurance, then it is permissible to deduct a portion of it equivalent to what you owe.