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Microsoft has all but stopped using product keys for anything. Your license is tied to your MS account which, at least for WIn11, is required. When you create your MS account on the machine the first time it'll pull your WIndows license from there. From that point on whenever you reinstall WIndows it'll get your license from your MS account. There is no need to track product keys anymore.
As for whether Windows itself is available to your version of Education though I cannot answer. Historically you needed to select the option to get student access, if you don't have it already. That takes you to the student activation section where you have to provide valid student email address so it can verify you are an educational student. Then Windows becomes available. If you don't have a student email or aren't a student then the Education software isn't for you. Education software is licensed for the use of education only and not for general purpose use. Refer to the licensing agreement as to what is and is not allowed to be used.