Middleware makes the actual APIs kind of irrelevant.
Also there is no OpenGL or Vulkan on majority of game consoles. Even on Switch, Nintendo still has their own API with much more lowere level control than Vulkan, just in case.
FWIW the PS3 (among others) actually offered OpenGL, not that you'd want to use it (the implementation was pretty bad - Apple-quality).
You can also theoretically run OpenGL code on the PS4 or XBox One if you want to, since they use well-understood AMD GPUs. Fail0verflow has already booted real OpenGL on hacked PS4s (via Mesa, I believe).
You can also run OpenGL on some platforms by using ANGLE to emulate specific versions of OpenGL on top of other APIs.
So, ultimately the "there is no OpenGL or Vulkan" observation isn't that meaningful - if your codebase is built around OpenGL, that's not necessarily a problem at all.
I don't know if I'd bother, but I'd also put money on it being possible to run ANGLE or Mesa GL on top of the PS4 graphics stack (I'm familiar with it).
As for the rest of your examples, they are workarounds, not official support, which means extra development cost when problems arise.
DirectX, PSGL, NVNAPI, and Metal are already available where Vulkan will probably never be.