If you have graduated and are currently working on OPT, it may be better to show proof of employment. This will prove that you are maintaining valid legal F-1 OPT status.
Well unpaid internships are a sham at times. Such an arrangement is allowed only if there are other workers (like citizens or green card holders) who are doing unpaid internship.
So it would be ok at Red Cross but not ok at Google. It may give the look that the company is getting a labor for free or that you are part of it only to avoid OPT unemployment rules.
In your specific case take the docs you have like employment letter and hope that the consulate doesn’t ask for payslips or client letter or does background check on such a work arrangement.