Not quite true, although it tends to be used a lot as Vulkan sales pitch.
Nintendo uses Vulkan on the Switch, but they also have their own Metal like API, NVN.
Vulkan is mostly used by PC ports into the Switch.
Exclusive Switch titles do so via NVN, Unreal or Unity bindings to NVN, not Vulkan.
Android has optional support for Vulkan, since only flagship devices ever bothered to actually provide it, with Android 10 Google has changed it into compulsory API. So only Android 10 or later devices are guaranteed to actually have proper Vulkan drivers available.
Windows supports Vulkan on the classic OpenGL ICD driver model, not available in Win32 and UWP sandboxes, which only allow for DirectX based code.
This is the actual reality, and not that typical Vulkan sales pitch.