The way you use the term “social contract” or “social agreement” somehow implies arbitrariness (at least to my understanding, correct me if I am wrong) . And while I agree Money is a social institution, it is not an arbitrary agreement. Money is selected for very specific reasons (portability, divisibility, etc… ) based on specific human knowledge.
Although the definition of gold has changed throughout history (the scientific specification), which means that the specification does not accurately point to gold, the market always knew what gold was. We could qualify the specification as a social agreement (I´d prefer scientific consensus of gold definition) But the knowledge of how gold fulfills the individual needs is beyond scientific consensus / social agreement.
My take on this issue: