Question: How long was the confrontation the USS Barataria saw as part of the Cold War?

Context paragraphs:
Aftermath of World War II: The aftermath of World War II was the beginning of an era defined by the decline of the old great powers and the rise of two superpowers: the Soviet Union (USSR) and the United States of America (USA).  Allied during World War II, the USA and the USSR became competitors on the world stage and engaged in the Cold War, so called because it never resulted in overt, declared hot war between the two powers but was instead characterized by espionage, political subversion and proxy wars. Western Europe and Japan were rebuilt through the American Marshall Plan whereas Eastern Europe fell under the Soviet sphere of influence and eventually an "Iron Curtain".  Europe was divided into a US-led Western Bloc and a Soviet-led Eastern Bloc.  Internationally, alliances with the two blocs gradually shifted, with some nations trying to stay out of the Cold War through the Non-Aligned Movement.  The Cold War also saw a nuclear arms race between the two superpowers; part of the reason that the Cold War never became a "hot" war was that the Soviet Union and the United States had nuclear deterrents against each other, leading to a mutually assured destruction standoff.

Cuban Missile Crisis: The Cuban Missile Crisis, also known as the October Crisis (Spanish: "Crisis de Octubre" ), the Caribbean Crisis (Russian: Карибский кризис , "Karibskij krizis"), or the Missile Scare, was a 13-day (October 16–28, 1962) confrontation between the United States and the Soviet Union concerning American ballistic missile deployment in Italy and Turkey with consequent Soviet ballistic missile deployment in Cuba.  The confrontation is often considered the closest the Cold War came to escalating into a full-scale nuclear war.

Soviet minesweeper T-112: T-112 was a minesweeper of the Soviet Navy during World War II and the Cold War.  She had originally been built as USS "Agent" (AM-139), an "Admirable"-class minesweeper , for the United States Navy during World War II, but never saw active service in the U.S. Navy.  Upon completion she was transferred to the Soviet Union under Lend-Lease as "T-112"; she was never returned to the United States.  The ship was renamed several times in Soviet service and was finally abandoned in January 1991.  Her hulk was extant as of 10 June 2007 .  Because of the Cold War, the U.S. Navy was unaware of the ship's status and the vessel remained on the American Naval Vessel Register until she was struck on 1 January 1983.

USS Barataria (AVP-33): The second USS "Barataria" (AVP-33) was a United States Navy "Barnegat"-class seaplane tender in commission from 1944 to 1946.  She saw service in the later stages of World War II and was decommissioned postwar.  She then was transferred to the United States Coast Guard and was in commission as the Coast Guard cutter USCGC "Barataria" (WAVP-381), later WHEC-381 from 1949 to 1969, serving in the Cuban Missile Crisis and the Vietnam War during her lengthy Coast Guard career.

Culture during the Cold War: The Cold War (1947–91) was reflected in culture through music, movies, books, television and other media, as well as sports and social beliefs and behavior.  One major element of the Cold War was the threat of a nuclear war; another was espionage.  Many works use the Cold War as a backdrop, or directly take part in fictional conflict between the United States and the Soviet Union The period 1953–62 saw Cold War themes first enter the mainstream culture as a public preoccupation.  For the historical context in America see United States in the 1950s.

List of military conflicts spanning multiple wars: Early histories of a war typically describe the war as it was declared by the states involved.  It is not uncommon for later historians to group together a series of wars over a long period or spread over several theaters as part of a broader conflict or strategic campaign.  The most familiar of these in the present day is probably the Cold War and the War on Terror, which included the Korean War (1950–1953) (Cold War), the Vietnam War (1965–1973) (Cold War), the Persian Gulf War (1990–1991) (Cold War), the War in Afghanistan (2001–2016) (War on Terror), and the Iraq War (2003–2011) (War on Terror) to name these five wars during the Cold War and the War on Terror.  These groupings provide useful context for the wars involved.  Note that some groupings overlap time periods and its possible for more than one war to be going on at the same time.

Soviet minesweeper T-111: T-111 was a minesweeper of the Soviet Navy during World War II and the Cold War.  She had originally been built as USS "Advocate" (AM-138), an "Admirable"-class minesweeper , for the United States Navy during World War II, but never saw active service in the U.S. Navy.  Upon completion she was transferred to the Soviet Union under Lend-Lease as "T-111"; she was never returned to the United States.  The Soviets later scuttled the ship in the Barents Sea in 1956.  Because of the Cold War, the U.S. Navy was unaware of this fate and the vessel remained on the American Naval Vessel Register until she was struck on 1 January 1983.

Soviet minesweeper T-120: T-120 was a minesweeper of the Soviet Navy during World War II and the Cold War.  She had originally been built as USS "Assail" (AM-147), an "Admirable"-class minesweeper , for the United States Navy during World War II, but never saw active service in the U.S. Navy.  Upon completion she was transferred to the Soviet Union under Lend-Lease as "T-120"; she was never returned to the United States.  "T-120" was sunk by "U-739" in the Kara Sea in September 1944.  Because of the Cold War, the U.S. Navy was unaware of this fate and the vessel remained on the American Naval Vessel Register until she was struck on 1 January 1983.

Cold War II: Cold War II (also called the New Cold War, Second Cold War and Cold War 2.0) refers to a renewed state of political and military tension between opposing geopolitical power-blocs, with one bloc typically reported as being led by Russia and/or China, and the other led by the United States or NATO.  This is akin to the original Cold War that saw a global confrontation between the Western Bloc led by the United States and the Eastern Bloc led by the Soviet Union, Russia's predecessor state.  American political scientist Robert Legvold posits that the "new Cold War began the moment we went over the cliff, and that happened with the Ukraine crisis."  Others, such as Andrew C. Kuchins in 2016, believe that the term is "unsuited to the present conflict," but the situation is arguably more dangerous than during the original Cold War.  One of the primary features of the "New Cold War", as first defined by Philip N. Howard, is that conflict is experienced primarily over and through broadcast media, social media, and information infrastructure.

Observation Post Alpha: Observation Post Alpha, OP Alpha or Point Alpha was a Cold War observation post between Rasdorf, Hesse, in what was then West Germany and Geisa, Thuringia, then part of East Germany.  The post overlooked part of the "Fulda Gap", which would have been a prime invasion route for Warsaw Pact forces had the Cold War erupted into actual warfare.  It was abandoned by the military in 1991.  Today, the "Point Alpha" memorial commemorates the Observation Point's four decades of existence.  The memorial is dedicated to keeping it and a nearby section of the inner German border as reminders of the division of Germany and the confrontation between NATO and Warsaw Pact in the Cold War.

Supporting paragraphs: USS Barataria (AVP-33) Cuban Missile Crisis
Answer: 13-day