Got a C in a sophomore subject unrelated to my desired major... how does this affect Ivy/Oxbridge chances?

Yea, it’s not good for Harvard/Yale. If the test-optional trend continues, your transcript will be even more important. Even pre-covid, you basically needed a perfect GPA to be competitive (unless you were URM or athletic recruit or major donor).

Also agree w upthread that CS is not exactly “unrelated” to Econ.