To piggyback on, the AUMF also explicitly mentions that it is the Act required in accordance with the earlier War Powers Act. They really leave it crystal-clear that the AUMF is very much intended to give the President the "Commander-in-Chief for a declared war" powers that Congress is able to grant.

It's horribly over-broad and open-ended, but Congress has only themselves to blame (and they can rein in the Act if they wish as well, or at least make the President try to veto it).