Well, the answer to this one has to be zero, right??? According to the War Powers Report submitted to Congress by the White House in December, the answer is “a small number”. The summary letter I have linked to also lists other deployments the U.S. considers part of its “counterterrorism” efforts in the greater Middle East. So the “war on terror” is very much continuing. Most of this is about combating “ISIS” and “ISIL”, more or less at the invitation of the host government. These groups are not “Iran-backed” as far as I know, and in fact are even threatening to Iran.

The U.S. is also sometimes attacking Iran-backed groups and Iranian military advisers under the umbrella of counterterrorism. This particularly catches my eye:

As reported on November 22, 2023, I directed United States forces to conduct discrete strikes on the night of November 21, 2023, against facilities in Iraq used by the IRGC and IRGC-affiliated groups for command and control, logistics, and other purposes.  These strikes followed attacks against United States personnel and facilities in Iraq and Syria that threatened the lives of United States personnel and Coalition forces operating alongside United States forces, and that were perpetrated by the IRGC and militia groups affiliated with the IRGC.  A United States contractor suffered a fatal cardiac incident while moving to shelter during one of these attacks.  I directed these discrete military actions consistent with my responsibility to protect United States citizens both at home and abroad and in furtherance of United States national security and foreign policy interests, pursuant to my constitutional authority as Commander in Chief and Chief Executive and to conduct United States foreign relations.

whitehouse.gov

I’ll try: “Iran-backed” groups are fighting “US-backed” groups in various countries. Iran and the US both have military advisers in various countries. U.S. troops and contractors are occasionally getting hurt in attacks maybe aimed directly at them, and maybe aimed at more local parties. We’re there because they are fighting us, and they are fighting us because we’re there.