I didn't found any information in the datasheet of ADSP-SC589 about the RTC current consumption
The ADSP-SC589 processor is part of the new, high-performance, power-efficient, real-time series that delivers greater than 24 giga-floating-point operations...
ADSP-SC589 on Analog.com
As per EE-392: Estimating Power for ADSP-SC58x/2158x SHARC+ Processors (Rev. 1), the VDD_RTC (for the Real-Time Clock) power domain is a marginal contributor to total power and can be ignored when calculating the full power profile for an application.
You can also refer to the following EZ post (same concept applies for the ADSP-SC589): https://ez.analog.com/dsp/sharc-processors/adsp-sc5xxadsp-215xx/f/q-a/64019/adsp-sc587-vdd_rtc-current-consumption
I hope this helps.