Article 1, Section 8, Subsection 3 (regulate commerce w/ foreign nations)
Article 2, Section 2, Subsection 2 (power to assign treaties w/ foreign nations)
Article 6, Subsection 2 (all treaties made are to be honored)
Absolutely none of those you cited authorize Congress to take American tax dollars and bestow them on a foreign country for humanitarian purposes or as essentially bribes.
Foreign aid is commerce? Foreign aid is a treaty meaning approved by 2/3 of the Senate?
You are going to have to do much better than that.
There may well be certain “costs of doing business” associated with foreign commerce, but that is not foreign aid.
Hint: The authorization ain’t there.