There's a couple companies out there that will port your game to consoles for you. [1]
https://docs.godotengine.org/en/stable/tutorials/platform/co...
The Switch does support Vulkan but it still leads to the problem of the walled-garden and NDAs which has already been discussed here at length, and also prevents any further abstraction layers for consoles from being developed by anyone besides these approved middleware companies. If the open source aspect is important to you then I would suggest avoiding these walled-garden consoles completely.
I don't think the console manufacturers have many incentives to work too hard on supporting these shared APIs. Their business models make it much more valuable to provide higher performing and more specialized code that works better on their console. And that price generally ends up being pretty small and well worth it for a team maintaining their own engine. And that math only becomes more insignificant the more teams are switching to the main engines such as Unity and Unreal.
I don't think your second paragraph is quite true and it's only because Vulkan is already supported on one of the consoles (Switch) and has been promoted by them for years as a way to make it easier for PC developers to port their games. There are also things like MoltenVK (which was a prime motivator for Vulkan support in Godot) that prove that there is some demand AND that other companies are willing to pay the expense of maintaining it, so it's not something that has to cut into their business model or mess with other products either.
Even if it is now finally supported, most of the game developers I know of are using the NVN backend.
I really like Godot. It's not as full featured as other engines but it feels very logical and clear.