> int is not nullable and Integer is nullable, and they are thus different types under the hood

Yes and no, because in Java we have runtime types and compile-time types. The frontend compiler will treat these types as having different defaults on nullability, but they'll compile down to the same representation (when appropriate). I.e. if the compiler sees that some Integer variable is never null, it will compile down to the same thing it would if it were declared an int.

You're right, however, that on the heap, until the language adds nullability information, the compiler cannot generally know that an Integer will never be null (unless it's a final field), so it's likely that, unlike on the stack, you'll get a different representation.