What is the period that one must wait before disposing of money found in a supermarket, given that its owner has not come forward and the supermarket manager has taken possession of it?

The amount you found is considered a lost item (Luqata). If it is valuable, you must publicize it for a year, after which the finder may dispose of it, based on the saying of the Messenger of Allah, peace and blessings be upon him: "Recognize its tie and its strap, then publicize it for a year. If it is not claimed, then spend it, and let it be a trust with you. If its owner comes seeking it one day, then hand it over to him." However, if it is of trifling value, you may take ownership of it immediately. The finder must not mention the gender or type of the lost item when publicizing it; rather, they should say: "O one whose item is lost." Therefore, you must continue publicizing the lost item until a full year has passed, then you may dispose of it. The supermarket manager does not have the right to take it from you. You should not have informed him of the amount, but rather of the presence of a lost item. You can post an announcement to that effect in the supermarket.