I am able to get the current approval step name using below API call.
OPTASK/search?fields=ID,name,approvalProcessID,currentApprovalStepID,currentApprovalStep:name&approvalProcessID_Mod=notblank
Hope this is what you are looking for. Please add or remove the filter in the end if you dont need it(&approvalProcessID_Mod=notblank).
Please mark my reply as "Correct Reply" if this helped you and to help others.
Thanks in advance!