As far as I am aware (but I could be wrong), there is no academic journal or book publisher that does not include footnotes into the total word length. Even if this is an essay, it is highly likely that your teacher also considers footnotes as part of the total word length. I advise you to confirm such details with the person in charge of the course.
There is no fundamental relationship between a citation style (or manual of style) and the length of footnotes. It depends on the topic that is being handled, and the chosen method of research. Longer-than-usual footnotes are more closely associated with certain research fields, especially within the humanities.
The most common use of extensive footnotes can be found in critical editions of pre-modern, medieval and ancient authors. A good example is the critical edition of the Dead Sea Scrolls, and a more recent example would be Sonu Shamdasani's annotated edition of Carl Jung's Black Books.
Related to this, we can find academic journals that allow for extensive footnotes (within reason), depending on the topic: studies of pre-modern legal history, religious texts, archaeological finds, medical treatises, ancient architecture, etc. One journal that tends to allow for large footnotes is Monumenta Serica (example 1) (example 2).
Lengthy footnotes tend to become unavoidable when one is dealing with cultures that are profoundly different from modern ones, or when dealing with artefacts and documents that go back far in time. Other fields such as philosophy can also sometimes have unusually long footnotes. Again, it depends on the topic that is being analyzed.
However, it is important to stress that one should make every possible effort to avoid long footnotes, even when it is allowed. For example, make a list of the topics or concepts that require the longest explanations, and create a section near the introduction that provides a basic, clear and simple explanation of such concepts. Then, when you need to add more nuance or minor details to those explanations, use footnotes. Or try to spread the explanation of those concepts throughout the text, while still using footnotes for small details. At every stage of the process, ask yourself: "Is this explanation really necessary for a reader to understand the key points of my essay?" Train yourself to write clearly and concisely, because that is one of the main reasons why students are asked to write essays.
One last word regarding styles. It has become fairly common to use Chicago (or adapted versions of it) in books with extensive footnotes, not because it encourages such long footnotes, but because it is designed to provide detailed referencing data for finding old documents in historical archives. Chicago is extremely useful when you need to distinguish between different manuscript copies or versions of the same text, which can be spread over different archives around the world.