Both DTLS and TLS still use it, but that will change in the following
commit. This also removes the handshake's knowledge of the
dtls_clear_incoming_messages function.

(It's possible we'll want to get rid of begin_handshake in favor of
allocating it lazily depending on how TLS 1.3 post-handshake messages
end up working out. But this should work for now.)

Change-Id: I0f512788bbc330ab2c947890939c73e0a1aca18b
Reviewed-on: https://boringssl-review.googlesource.com/8666
Reviewed-by: Steven Valdez <svaldez@google.com>
Reviewed-by: David Benjamin <davidben@google.com>