`extension/public/api.h` currently uses types such as `enum`, `int`, and `size_t`. However, different systems will have different widths for these types.

This ticket should swap these types out for fixed width types such as `uint32_t`, `int64_t`, etc.

See https://github.com/10gen/mongo/pull/40091#issuecomment-3192718311 for more information.