Sean
Power electronics side ground is the normal ground for electrical safety.
Shielded ground on the pendant side is for the screen on the cable between the control pendant and the VFD. Everything pendant side is low voltage so no safety issues. Shielded cable is advised to minimise any chance of picking up electrical interference.
Leaving it hanging is probably normal unless there are serious control electrical noise issues. In that case you'd need skilled folk with all the test gear to sort it out. Not something you'd need to worry about in any normal home shop installation with the inverter close to the machine and nice short cables.
Pendant arm itself would normally earth via the machine but Inspector Meticulous on a cranky day might consider an extra wire desirable. But realistically only necessary on old style high voltage contactor control machines (Holbrook, my P&W et al).
Clive