There was a lot to unpack there!
Obviously, we wouldn't add operations for WWII because it's already the name of the war/operation in itself. But for things like OJE, OJG, and so many others, I believe a category is needed . Now breaking these down further by unit is perhaps not necessary, at least until/when we have hundreds of profiles there and need to break them down.
I was doing a bit more research. Wikipedia calls these "military operations other than war" (MOOTW) which might be a good parent category and could be broken out further by country. These newer types of conflicts are the way things go these days, troops still go, serve, have hardships, and die during them. In fact, because the FRY was so unstable when we first went in, initial OJE participants were given the Expeditionary Medal, until the operation was stable and renamed OJG. That's why I have that medal and qualify for the VFW.
Here are a few others since the Vietnam War:
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Operation Eagle Pull (1975): Evacuation of Americans from Cambodia during its fall.
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Operation Frequent Wind (1975): Evacuation from Saigon at the end of the Vietnam War.
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Operation Urgent Fury (1983): Invasion of Grenada.
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Operation Just Cause (1989): Invasion of Panama to depose Manuel Noriega.
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Operation Provide Comfort (1991): Humanitarian relief to Kurds in Northern Iraq after the Gulf War.
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Operation Restore Hope (1992-1993): Humanitarian mission in Somalia.
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Operation Uphold Democracy (1994): Intervention in Haiti to restore democratic government.
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Operation Joint Endeavor (1995-1996): NATO peacekeeping in Bosnia and Herzegovina.
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Operation Allied Force (1999): NATO bombing campaign in the Kosovo War.
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Operation Enduring Freedom - Philippines (2002-2015): Counter-terrorism and training mission in the Philippines.
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Operation Unified Response (2010): Humanitarian response to the Haiti earthquake.
I'm off-subject a bit. If I understand correctly, the purpose of a category is to group people by place, event, occupation, and so forth, so we find others and make connections. Many categories are currently broken down into tiny groups, such as a little masonic lodge in "BFE" that I saw the other day That's fine with me; if there is a category, people will eventually use it. As long as one profile holds down the category it won't be deleted and will be there for others to add to. We need to look to the future. At some point, our descendants will be looking at our profiles and interested in how many of their ancestors participated in this or that and perhaps placing our profiles into categories. Right now, I'd prefer to do that on my own profile myself. My record may not be adequately published. I have ancestors who served in WWI and WWII for whom I can't even find a unit. I'm speaking for myself but if we ALL don't build out our own bio fully and correctly, who will?
Too many genealogists ignore their own biographies, IMO.
And yes you should apply for a Cold War certificate.