@Riley_S Thanks, Riley. 

The situation has improved.  I did the following:

• Removed the switch from the app
• Turned-off power at the circuit breaker
• Turned-on power at the circuit breaker
• Add the switch back to the app

Now, when the lights are off and the Lutron Diva "dumb" dimmer is at maximum brightness:

• I can control the lights from the app and the status in the app is correct (good)
• If I turn the Lutron Diva switch on or off the status of the lights in the app does not change (bad but tolerable)

When the lights are off and the Lutron Diva "dumb" dimmer is at minimum brightness:

• The 1st switch of the lights in the app causes the status to indicate the lights are on but the lights are still off
• The 2nd switch of the lights in the app causes the lights to turn on and the app status still indicates the lights are on
• The 3rd switch of the lights in the apps causes the lights to turn off and the app status indicates the lights are off

This is actually good enough for my purposes since I intend to have the lights at full brightness on a schedule.  I confirmed that the Kasa scheduler does reliably turn the lights on or off when the Lutron dimmer is at maximum brightness.

I considered buying a Kasa smart 3way dimmer pair of switches but I'm happy with my Lutron dimmer and I noted on Amazon that the Kasa 3way dimmers are often returned.