To answer your question -
The reason we dropped DirectX 12 support in new versions of Dolphin is because when we added DirectX 12, we thought that we could keep it working and fix bugs that appeared. We could not do this. The back end was written in a way that made it very hard to fix and nobody wanted to put in the effort to fix it. The developer that wrote the back end also left. The back end was also stopping us from improving certain parts of Dolphin because nobody wanted to also implement some fixes in DirectX 12 as well as the other back ends we supported. So we dropped it.
Recently, a developer has been putting in effort to rewrite the part of Dolphin that handles graphics to make graphics back ends easier to manage and fix. So we could support experimental back ends like that again. But this will not happen for a long time, so do not get your hopes up.
Vulkan is a back end that is like DirectX 12, except that it works on any operating system Dolphin supports, and was written in a way that makes it easier to fix bugs. The only down side to Vulkan is that some GPUs have drivers that do not work well with Vulkan. DirectX 12 had better drivers.
I tried to write this reply in a way to make it easy to translate.
The reason we dropped DirectX 12 support in new versions of Dolphin is because when we added DirectX 12, we thought that we could keep it working and fix bugs that appeared. We could not do this. The back end was written in a way that made it very hard to fix and nobody wanted to put in the effort to fix it. The developer that wrote the back end also left. The back end was also stopping us from improving certain parts of Dolphin because nobody wanted to also implement some fixes in DirectX 12 as well as the other back ends we supported. So we dropped it.
Recently, a developer has been putting in effort to rewrite the part of Dolphin that handles graphics to make graphics back ends easier to manage and fix. So we could support experimental back ends like that again. But this will not happen for a long time, so do not get your hopes up.
Vulkan is a back end that is like DirectX 12, except that it works on any operating system Dolphin supports, and was written in a way that makes it easier to fix bugs. The only down side to Vulkan is that some GPUs have drivers that do not work well with Vulkan. DirectX 12 had better drivers.
I tried to write this reply in a way to make it easy to translate.