One of the GZDoom developers, dpJudas, has been working diligently on the Vulkan [GitHub] renderer for GZDoom.
I have tried it out myself and at this point it seems to be coming along nicely, but there are still many loose ends that need to be taken care of, which is only to be expected of such an early work in progress. For example, alt-tabbing out of a full screen window and back into it will make the game crash.
The developers have said that the Vulkan renderer will not bring a significant performance boost to GZDoom, so it sounds like Vulkan is being added for future-proofing and improved macOS support with MoltenVK. From what they said in the comments of the GZDoom 3.7.0 release announcement:
Don't expect any miracles from Vulkan. It cannot overcome the main problem of the renderer, i.e. that major parts of it need to be run in sequence. The entire renderer has two barriers where each side can run independently of each other. I was able to multithread one of these barriers, the second one will be a lot harder. In OpenGL it can only be done by using GL 4.5 features plus one extension.
And it's this second barrier where Vulkan would come in and allow more efficient handling - but even so, this won't result in a magical speed up but more likely increase performance by 15-20% at best, maybe.
In order to use the Vulkan renderer, you need a version of SDL2 that supports Vulkan as well as a custom Vulkan build of GZDoom.
It's possible, but uncertain, that the Vulkan renderer will be in the next release of GZDoom. Either way, it's definitely something to keep an eye on.