[I_Am_Nous]

The President is the Commander-in-Chief of the United States Military. Currently, European leaders are discussing sending peacekeeping troops to Ukraine, but the UK has claimed they will only send troops if the US promises to provide a "backstop".

So a lot of the power of the President to direct foreign policy is because they essentially control the military and many other countries rely on the US military for a lot. On the other hand, if you anger the US, the President can decide to change tactics suddenly such as Obama increasing the use of drone strikes or Trump using NATO as a bargaining chip.

The US is still looked upon as the final say in military situations because it also has the largest military in both active combat forces and equipment.There is an expectation that the US will act as world police - I remember Obama catching grief over not intervening in Syria. All of this adds up to America being "the big stick" and has somewhat changed the Presidency. This is also why Isolationism vs Interventionism is such a heated debate.