When the ignition is turned to the on position and the dash lights come on temporarily the check engine light does not come on?

This is still a lot of codes, are you having any issues with any of these components? And just so you know, the module listed in black above is the module reporting the issues with the circuits or communications to other modules in red. So, I see some Radio codes, HVAC, ABS, SRS, are you having any issues with these systems or lights on for them?
I see a lot of Lost comms with Cluster, I think that is the Cluster having the issue and not these modules, they are just reporting that they're not getting a response when pinging the Cluster.
Does your other scan tool report like this?

Well, the lost comms is only with those specific modules that are setting a code for it. If the Cluster was completely offline the PCM and other modules would be setting the same code. The GMLAN low speed network is divided up into sections, so there could be a network splice that has some corrosion or resistance in the circuit causes those networks to set the codes. The 1st diagram below shows all the low speed 1 wire network which has all the lower priority modules on the Green wiring. The 2nd diagram is the GMLAN high speed 2 wire canbus type network for the high priority modules, PCM, TCM, ABS, etc, due to safety.
The HVAC has quite a few temperature sensors that feedback to the HVAC module, we can try to track down the circuit issue if you want to get some heat going in the vehicle. You could go into that module and check the live data for the temperature sensors, one of them will be reading far out of range compared to the others, the module probably defaults or shuts down when codes like that set. With the Auto A/C system, I'm seeing about 9 temperature sensors, some are for the rear HVAC system. If you can find a sensor that is out of range, that's the one we could try to find and get some heat going. Or wait until fall if you want. I'll check that code out though. As for the MIL, I know that LEDs have to have a current limiting resistor in series with them or they will burn out. So, if that PCM control circuit shorted to ground and the protection resistor is in the PCM on that control ground circuit, I can see the test light staying on more than the 30 seconds and it burning out the LED. I have burned my share of LEDs building circuits,

There was actually 3 TSBs on that code, it calls for a reprogram the HVAC module not replace it, so that would be good if its just a software glitch.
It actually looks like this B0433 is for the rear Aux air temperature actuator. Not sure why its effecting the front hvac, technically it should only disable the rear aux actuator, so it might just be a reprogramming issue.