Is providing the difference between the agreed-upon salary in Syrian Pounds and its equivalent in US Dollars - due to the high exchange rate - considered permissible or forbidden?

Your agreement with the worker to adjust the salary according to the exchange rate periodically, without specifying the duration, involves gharar (uncertainty) and jahalah (ambiguity), which makes the wage unknown. This is impermissible, as one of the conditions for the validity of ijarah (leasing/hiring) is that the wage must be known. Therefore, they are entitled to a wage of similitude (أجرة المثل) for the work they have performed, to be estimated by experts. If the wage of similitude exceeds the agreed-upon wage, they are entitled to the increment, unless they consent to forgo it. You must rectify the contract with them in the future by specifying the wage.