The "operation is over" framing is contradicted by what Hegseth and Caine said at the Pentagon hours earlier on the same day:
Iran fired at US forces 10+ times since the ceasefire; the US naval blockade of Iranian ports remains "in full effect" (Hegseth's own words); six Iranian vessels were turned back today; US Apache helicopters and Navy MH-60s are actively defending against Iranian cruise missiles, drones, and small boats. CENTCOM "remains ready to resume major combat operations against Iran if ordered to do so" (Caine, same day). An operation that has 15,000+ active service members in theater, an active naval blockade, daily kinetic engagement, and explicit readiness to resume major combat is not a "concluded" operation.
Renaming it does not end it for War Powers purposes.
Sources: CNN live (Rubio quote) · Pentagon briefing transcript May 5 (Rev.com) · 50 U.S.C. §1544