The Supreme Court participates in matters of foreign policy primarily through judicial review, specifically by interpreting constitutional law related to the actions of the legislative and executive branches. It can decide cases that involve the separation of powers, evaluating whether actions taken by the president or Congress are constitutional. However, the Court does not directly oversee military actions, approve treaties, or have a role in the appropriation of funds, as those responsibilities lie with the legislative and executive branches.
In summary, the Supreme Court's primary involvement in foreign policy is through its power of judicial review, assessing cases that concern the limits of executive power and the constitutionality of laws and actions relating to foreign affairs.