[libc++] Clean up includes of <__assert> (#80091)

Originally, we used __libcpp_verbose_abort to handle assertion failures.
That function was declared from all public headers. Since we don't use
that mechanism anymore, we don't need to declare __libcpp_verbose_abort
from all public headers, and we can clean up a lot of unnecessary
includes.

This patch also moves the definition of the various assertion categories
to the <__assert> header, since we now rely on regular IWYU for these
assertion macros.

rdar://105510916