[HIP] Fix `--no-offload-new-driver` behavior after #201457 (#205094)
Summary:
https://github.com/llvm/llvm-project/pull/201457 changed the default for
all targets. Even though the old offload driver is getting removed soon
we shouldn't break it for the LLVM23 release. This simply reverts to the
original behavior, the old driver builds its jobs manually so we can
just turn off this one specific case unless the user forced it.