The issue was caused by the duplicate addition of the Content-Type header due to the call to doAddHeaderValue in the else clause of the MockHttpServletRequest#addHeader(...) method.
This behavior is scheduled to be fixed in Spring Framework 6.2.8.
📌 This was not an issue caused by the combination of RestAssured and Spring REST Docs.
In the actual execution, it is presumed that the same spec definition was added more than once, resulting in duplicate headers being passed to Spring Test.
The modified code resolving this issue is available in the refactor branch.