The TS-480 and the TS-590 both use the same CAT command for power on: PC1;
The difference seems to be in the Hamlib implementation of that command, Hamlib being the underlying engine for CAT control in the RigPi.
You found that power on works when you selected TS-480 as your radio and I had not tried that myself.
I do have a TS-590s here but I normally use a different radio and my desk has space for one radio/amp/speaker/panadapter at present.
I never experienced latching PTT in the TS-590s. Other TS-590 users have reported that issue, so it can happen.
Do you have the latest 2.04E firmware installed in the radio?
There is a RigPi software update coming that has several improvements including a fix for the latching PTT, expanded TX control and multi command macros.
73 - Mark - K8MHW
'A RigPi Enthusiast!' - I am not otherwise affiliated with MFJ or RigPi