"Accessibility" is the word you're looking for.
In the context of tech, the word "accessibility" now refers exclusively to assistive technologies, technologies to assist differently abled people, like on my Sony Bravia, if I want to find the options for closed captioning, I find them in the "Settings" menu under the submenu "Accessibility."
Note that "accessibility" is a different word than "accessible," "inaccessible," and "access," all alternate words you mention. While the root word "access" is the same, all other forms of the word "access" are still used more generically, like in your example, "...the button is not accessible/inaccessible."
In tech, whether it be websites, phones, smart TVs, or whatever, "accessibility" is the keyword used for referring to assistive technologies for differently abled people, and it is used exclusively for this purpose. All other forms of the word "access" continue to mean what they've always meant unless used in conjunction with and/or in a context that expressly refers to "accessibility."
So, as I said at the start, the word you're looking for is the one you gave: "accessibility." As long as you don't use "accessibility" in regard to tech with any generic sense but solely for referring to aspects of tech having to do with differently abled people, there will be no confusion because "accessibility" is the operative word in the context of tech. In tech, if one hears or reads "accessibility," one can rest assured that what's being discussed is assistive technologies for differently abled people, but if the word "accessibility" isn't anywhere present, isn't used to introduce what's being discussed, one can rest assured that "access" and all its other forms simply carry on meaning what they've always meant without any narrowing to just aspects having to do with differently abled people.
Yes, that means you may need to reword some things sometimes, like in a situation not having to do with differently abled people where you want to write, "The button is not accessible," like your example, you'd write exactly that instead of writing something like, "The button lacks accessibility," because you'd know that using the keyword "accessibility" throws up a flag for readers and would stand to imbue what you'd be saying with a meaning other than what you'd intend.
By the way, this use of "accessibility" may have started as jargon, but it's gone well beyond jargon and into the common vernacular as people in general are increasingly aware and expected to be aware of this special meaning for "accessibility" when it regards the tech they use every day, like how Sony expects me and all its customers, the general public, to simply know from reading the word "Accessibility" alone with no other cues or clues that selecting it is how you find any and all of the device's options having to do with differently abled people, like closed captioning options.