Seems like Compute Mode is not supported on Windows 7. This from this previous AMD Thread: Missing GPU workload option on RX580
According to this other old thread a reason why Compute Mode may not be visible as per AMD Moderator RAY_M is that settings already are optimized for computer mode, at least on the Vega64, in this thread:No GPU Workload option on AMD RX VEGA64 Sapphire Limited Edition
So either you RX590 is already optimized for Computer Mode thus not showing the feature or Windows 7 doesn't support that feature in the latest AMD Driver.
I went to my wife's computer that has a AMD GPU card (R7-360 series) on Windows 10 and that feature is not shown. possibly because the GPU card doesn't support that feature or is already optimized for computer Mode in my case.