[libc++][CI] Increases the Clang version used.

Changes the CI to use the Clang 16 nightly builds instead of Clang 14.
(The libc++15 branch was accidentally build using Clang 14 instead of
Clang 15; hence the skipping of a number.)

Also adds a Clang 15 build to the test matrix.

Based on the private discussion with @ldionne we decided to move
the configuration parameters from the `run-buildbot` script to the
CI configuration `buildkite-pipeline.yml`. Other hard-coded values
from the Dockerfile should be move to the CI configuration too. That
will be done in another commit.

C++17 will use Clang-15 since D131479 causes a test to fail.

Reviewed By: ldionne, #libc

Differential Revision: https://reviews.llvm.org/D131174