If debug logging was on there should be more info. Also the Events tab from the device page has good info in it, like showing exactly what commands were called from apps, and in what order.
Screenshots would be better than copy/paste for readability. Use Windows Snipping Tool.
Lutron's native integration to Apple Home definitely behaves differently. I normally like to minimize hops, but Lutron's native integration just is not good. I've got RadioRA 2 and almost none of my dimmers are set to come on at 100% at the switch. So using the native Lutron to Apple integration is not satisfying at all. Hubitat's Lutron drivers let you set the 'on' level to fixed or previous. And Hubiitat's integration with Apple Home uses those settings when turning on (so did the Homebridge integrations). Much better.
Ok thanks that givces all the info needed I think.
@JoeNY Please verify, you are just tapping the icon for the light to turn on/off correct? Not opening it and using the slider?
@gopher.ny is this intentional where it does On then setLevel right away or is that coming from Apple Home itself? For some reason the integration is sending a setLevel 100 to the device causing the lights to come on then ramp up to full brightness instead of the last brightness. I dont think I get this with the Homebridge plugin.
There was another user with a HomeKit issue yesterday. There were no good leads for the cause. I asked him to try removing/re-adding the device from/to HomeKit. It seems to have fixed his issue. You might try that.