Screen readers use the clear semantic difference between a button and a link to make sure the user knows what to expect and users are used to the different keyboard shortcuts. I saw in your specification an example where a website made effort to work around this clear separation and from what I could tell there may have been user testing, but in other places I see that usability is best for screen reader users where the semantics are clear.
This proposal would standardize an in between element, adding a third form they have to understand with different behaviors. I guess just make sure you get some experienced accessibility feedback in your submission.
I'm not entirely sure what you mean by "in-between" element, but that's not what this proposal does. This proposal simply augments the button's existing ability to navigate the current context by removing the need to wrap it in a form. This is useful because sometimes buttons are already the right semantic element to use, but you can't use them to do this without JavaScript.
Also, that link has a lot of wrong information and is not an official W3C site. It even has a LinkedIn page.[0]
[0]https://www.linkedin.com/company/thewcagcom/