In creating the Boggart, Mrs. Rowling seems to have lifted a word out of Celtic mythology,1 only to then entirely disregard the backstory that mythology would normally imply.
Level of Intelligence
Like the [Dementor], this is fairly debatable. Mrs. Rowling [tells] us of several boggarts that have taken on the shape of humans for fairly long durations.2 What she does not tell us is enough detail to know if these boggarts could pass a "Turing Test".
Analysis
Unlike the [Dementors], there are no obvious inconsistencies with the boggarts. That is not to say there are no concerns. These particular [non-beings] exemplify the problems with the [balance of power] more clearly than, I think, anything else in the books do. They can become anything, including having a reasonably effective facsimile of that something's magic (thus it can become a [Dementor]. Even if it is a somewhat weakened facsimile, the fact that it can resurrect a suppressed memory and cause [Harry] to faint means that it is still a frighteningly over-powered creature.
[Harry]: </Harrypedia/people/Potter/Harry James/>/ [tells]: https://www.rowlingindex.org/work/pmbog/ [Dementors]: /Harrypedia/non-beings/dementor/ [Dementor]: /Harrypedia/non-beings/dementor/ [non-beings]: /Harrypedia/non-beings/ [balance of power]: /Harrypedia/balance/
Footnotes
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Wikipedia "https://en.wikipedia.org/wiki/Boggart" Last Edited: 2021-10-04. ↩
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Mrs. J. K. Rowling. "Boggart" Publication Date: 2012-12-20. Last Viewed: 2021-10-21. ↩