The president doesn't really need Congressional approval to do much of anything.
Congress passed the War Powers Resolution (not an Act of Congress, you may note) in an attempt to limit the military powers of the Executive Branch... It has never been tested in the Supreme Court. (See Campbell v. Clinton which was not appealed by Congress to SCOTUS.... The district court granted the President's motion to dismiss for lack of standing, see Campbell v. Clinton, 52 F. Supp. 2d 34 (D.D.C. 1999))
In any event, it does not require the president to obtain Congressional approval prior to committing US military forces....
https://www.law.cornell.edu/uscode/text/50/chapter-33