Have they released an open source implementation of their Vulkan driver, or did I dream that? And didn't Nvidia promise something similar? Has anything come out of those promises?
No, they never released it. They said several times, that they are working on opening it though. They already replaced their previous shader compiler with llvm toolchain for example, but there is more work than that.
Meanwhile, radv is advancing pretty well. AMD never clarified what their strategy is in regards to radv. I.e. whether they plan to compliment it with their Vulkan driver, or they intend to make a second open one.