C++ (gcc), ^{280 \$\cdots\$ 277} 228 bytes

#import<bits/stdc++.h>
#define S(v)std::sort(v.begin(),v.end());
using V=std::vector<int>;V f(V&v){std::vector<V>w;S(v)for(int a:v)for(int b:v)for(int c:v)if(a+b+c==v.back()){V x={a,b,c};S(x)w.push_back(x);}S(w)return w.back();}

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Uses Jonathan Allan's idea from his Jelly answer

Inputs a vector of integers.
Returns the vector with the minimum difference between the smallest and the largest element from all the cartesian products of 3 elements that add up to the maximum of the input vector.