Why is nullptr a part of the core language, but nullptr_t is a part of STL?

Because it can. A central aim in the C++ standardization process is to alter the core language as little as possible when adding to the language.

nullptr usurps the use of 0 to mean both a null pointer and, er, zero. Using 0 for both caused problems for obvious reasons, does f(0) call f(int) or f(int*)? So a brand new literal was added to the core language: nullptr. Its type is simply decltype(nullptr) so nullptr_t was added as a short cut:

namespace std {
    using nullptr_t = decltype(nullptr);
}

The proposal that introduced nullptr, N2431, indicates in section 1.1 that it was desirable to not force users to include a header in order to use nullptr.

It also remarks, "We do not expect to see much direct use of nullptr_t in real programs". Thus, it was considered preferable to add nullptr_t to the library rather than create a new keyword only to be used for this obscure purpose. In addition, if you don't want to include the header, you can always just write decltype(nullptr) yourself.