Great question @tjodowd , I don't know of any accessibility API, but there are some tools who are using the Canvas API to do some of the functionality you are discussing. See Comparison of Canvas Accessibility LTI Tools for a few of those tools as well as the open source Canvas accessibility checker.
All of those tools check for missing alt text (at a page, course or institution level) and two of those services (Ally and UDOIT) use the YouTube API to check YouTube videos for captions.
In addition, there are other accessibility tools that can check content for accessibility such as axe (free) or WAVE (paid) that could in theory be integrated with Canvas to do this kind of work. Besides the above mentioned tools, I am aware of at least a couple of other upcoming tools that will provide similar accessibility functionality within Canvas.
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