Your right that the constitution does not give the executive this kind of power. However it does give the legislative the power to suppress insurrections/rebellions. They have done this by passing laws such as the militia acts in the 1790 as a result of the whiskey rebellion, and the force act during the nullification crisis. These acts delegated authority to the executive.
In 1861 and 1862 Congress passed the confiscation acts. This gave Lincoln the authority to issue the emancipation proclamation.
No matter how many times you neo-confederates claim Lincoln was a dictator he bent or broke the law surprisingly few times. I’d even argue maybe even less than other Presidents during times of war.
No, congress cannot give such a power to a President either.
You also do not explain how they can specify that only one type of property is "contraband of war", and none of the rest is. This is hiding the real fact, that this is not about "contraband", and is instead about making a specific political statement.
If the "contraband of war" claim is allowed across the entire population, the Federal government effectively owns everything in the area of rebellion. They didn't go that far because people would immediately notice this is a false power. By deliberately limiting this false power to "slaves", they kept people from pointing out that this cannot be a legitimate power under the US Constitution. Had they confiscated everything under this alleged power, the game would be up, and even the worst of them would not be able to deny this was a dictatorial move, and not a valid constitutional power.