ICE runs but does not show on Energy Monitor (2021 Prime)

I have seen lags on the display when the engine is on during the warm-up cycle. In your case, the engine came on because of the windshield defogger during EV mode, so that display is normal. If you switch to HV mode, then the engine will be lit and you will see the energy arrow flowing from the engine to the wheels.

 

First, car dash displays aren't scientific instruments. There will be lag, and even info the software deems unworthy of display at times.

As for the OP, my understanding of the Energy Monitor from a gen2 is that it shows where the energy is flowing to and from, not what component is on. The car appears parked in the photos. If not in drive, energy can't flow from the engine to the wheels. Then the battery appears near full. With that state of charge, or something else like temperature, the system has deemed charging the battery at this time isn't a good idea. So no flow from engine to battery on the monitor.

Then going back to the first point, there is energy flowing, but beneath the threshold that would have it be displayed on the screen.

 

On our 3rd gen, if the car is stopped with engine running, the displays show (incorrectly) that no gas is being consumed. Once you start rolling it goes back to showing gas consumption.

 

Then it could just be a bug. As @Mendel Leisk points, out the software could simply not be working as it should, which what fall under the not a scientific instrument category. The engine came on for the defogger, but you're in EV mode. The software for the Energy display may not show any activity from the engine because you are in EV mode.

Here's another you may not have noticed yet. There is a percent EV in the displays somewhere. The software running it is a carry over from the standard Prius. So it isn't showing a ratio of time or miles the car was in EV mode to HV mode. It is instead a percentage of how often the engine actually ran, regardless of mode.

 

When there is no load on the engine, it will not show any activity. That's the nature of the "Energy Monitor". It's just there to give you a general idea of how the system works. (KISS). That should be obvious, since there are 2 electric-motors, yet only 1 is displayed.

 

Aside from the puzzle over whether the ICE is actually charging the battery is the fact that it came on in the first place.

Apparently, you pushed the defrost button rather than changing the airflow to the windshield. That defroster button starts the ICE every time and is usually not necessary, especially in places like the SF Bay area.

 

I rarely use that "max" defrost even here in Minnesota. The regular electric-only does the trick most of the time.