I like that the writing here is simple and clean. I also like that the writing is friendly and informally (we and you) without being colloquial.
Most of the content is for someone with some experience with APIs already. Because of that, you may want the section on "About APIs" first, and then have the information specific to the Mediawiki API after it. This will helps folks discern whether the rest of the information is relevant to them. If they don't know what an API is, they information about specific APIs will have little meaning.
I made some corrections for grammar, but overall, there were few errors. Other editors may make changes to fix inconsistencies once you move the page into a more prominent space.
You may consider removing adjectives where you can. For instance, change "its use is strongly discouraged" to "its use is discouraged." The meaning here is the same, and we are looking to reduce and simplify where we can.
I ran the page through a tool to check the reading level: https://www.webfx.com/tools/read-able/flesch-kincaid.html It scored pretty well. This can be a good tool when working on documentation; just be aware that technical language and jargon can change the scores.