Why are cobalt deposits so unevenly distributed?
Part 1

The Democratic Republic of the Congo's Katanga Province contains
almost 40% of the world's reserves of cobalt [1].
Why are deposits concentrated so strongly in such a small portion of
the earth?

Cobalt isn't as unevenly distributed as it seems. It is correct that most of the world's cobalt reserves are in DRC, but most of the cobalt resources are not in DRC. And this is a very important point.
Resources are known and estimated quantities of economically extractable materials. Reserves are resources for which detailed plans for extraction have been made. This means that to turn a resource into a reserve you need to have plans for the extraction and refining plants, have environmental approval, have the workforce figured out, have authorisation from the owners of the land, and more. As you can guess, making a resource into a reserve is a time consuming and expensive process.
The reason why most of the Earth's reserves are in DRC is simply because it's easier and cheaper. The infrastructure already exists, and the expertise exists. At current technology levels and cobalt prices, the investment in defining a reserve from a resource elsewhere is simply not economical.
This does not mean that DRC has most of the cobalt. It only means that getting cobalt out of the ground and making it into a product is cheaper in DRC than it is in other countries.
Part 2

Do the geological processes causing this uneven distribution significantly differ from those that cause the uneven distribution of gold?

The reasons are the same, in principle. Every element behaves differently and will separate from other elements and concentrate because of various geological processes. Cobalt tends to follow copper and nickel, and in most cases it is mined as a by-product of those elements. That's why cobalt is extracted from the African Copperbelt, and why it's extracted from nickel deposits in Australia. Not much point going into the chemistry and thermodynamics of why this happens, but the point is that elements which are concentrated by rare geological processes will be found in fewer places, and elements that are concentrated by common geological processes will be found in more places.