Revert "[runtimes] Probe for -nostdlib++ and -nostdinc++ with the C compiler" (#113653)

Reverts llvm/llvm-project#108357

Breaks https://lab.llvm.org/buildbot/#/builders/164/builds/3908 and
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NOKEYCHECK=True
GitOrigin-RevId: 240e4780680f0d6a760be1b9ea432f410424b3a5
2 files changed