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

When did all those codes show up? No wonder the MIL is not coming on, there's all kinds of modules offline, due to low voltage. Have you checked the charging system? You might have a main bus fuse that has burned out, check the main fuses at the battery as well as all of the ones in the rest of the vehicle.

https://www.2carpros.com/articles/how-to-check-a-car-fuse

Well, there's a lot of codes there, I do see some lost communication codes. What codes come back after the battery was replaced? Because there are some random serial data codes such as the "Passenger Presence Module" - erratic and invalid serial data received, Battery Voltage below Threshold, Lost comms with Cluster, ECM problem exists, just a ton of codes that could be caused by low voltage,
Any computer is going to malfunction when its supply voltage is too low. So, the first thing to check is put a multimeter on the battery at idle and see what the charging system voltage is. You have a new battery now, so clear the codes, start it up, check the charging voltage and see what codes come back first. Turn some electrical loads on as well, headlights, rear defrost, AC, etc., those components will load the Alternator. If the Alternator is failing the voltage will drop with those loads on it. With a new battery right after start up you should see 13.6 to 14.2-volts roughly. If it starts to drop into the 12-volt range then the Alternator is not keeping up, or there is a wiring issue in between the battery and Alternator or the Alternator and the PCM which controls it.
If all looks ok with the charging system and codes come back, we'll have to check each one.
Unplugging the coil wouldn't set any codes except for that coils circuit, all these other codes could be low voltage, or a bulk connector might be corroded. I'll save the codes in your folder, so just clear them and see what happens with the new battery. There's no way to tell why it cut off on the tech, there's so many codes here.

https://www.2carpros.com/articles/how-to-check-a-car-alternator

I'm a bit confused here, you said you had tires and an alignment done, but there are all kinds of codes here for all 4 of the TPMS sensors. Also, are your seat heaters working at all? Or any issues with the power steering? Just going through this list of codes.

What I have noticed with every module setting codes is the U0155 code, I didn't get through all the codes yet, I left the tire pressure ones out, if they're working okay, we won't worry about that for now. The charging system isn't as high as I would like to see it, but it's also a new battery. So, let's see what codes are set in the next few days or so. Below are the modules setting each code and you can see that most modules setting codes are setting that U0155-lost comms with the Instrument Cluster. If you have cleared all the codes already is the Check engine light coming on now? Almost all these codes are voltage related, one of them which was very concerning was the C0900 which is the ABS module voltage above 16volts. But this can be a module malfunctioning due to low voltage, especially since the ABS module has solenoids that can turn off and on very quickly, that can induce a high voltage spike like that. As for the seat heaters, if you don't have them, then the scan tool was either reading and misinterpreting codes or setting them as some default. There might have been low voltage at the Data link connector at some point as well. Just let me know what happens with the new battery. I'm wondering if the Cluster might be failing and pulling the GMLAN data network down, that's a possibility as well. Just check for codes, even if the MIL is not on.

Can you access the Instrument Cluster through that scan tool? If it's able to read codes from it you should be able to get into those modules to see live data and possibly special functions.

There should be a function to turn on the MIL either in the Cluster module or PCM. Since the control wire is in the PCM, the function will most likely be under the PCM special functions.

Yes, it's listed under ECM, (engine control module), it looks like the modules are communicating. What scan tool are you using? Is that a Topdon? A PCM listing is Powertrain Control module and usually is an Engine control module and Transmission module in one unit.

I thought the check engine light was not coming on? Thats your original post. Does the light stay on after you start it?
With the Key Off, use a multimeter to see if pin 18 is shorted to ground. Just put one meter lead on pin 18 and the other on any ground. It shouldn't have a path to ground with the key off. If it does, the wire that runs from the Cluster to the PCM on pin 18 is shorted to ground somewhere.
The PCM had a MIL fault code stored, P0650 so the PCM was seeing that fault.

It should go out after about 30 seconds on most vehicles, have any of those codes come back? There was a lot of lost communication codes listed from different modules, including the cluster, but since the MIL looks to be a LED in that Cluster, it may have burned out if there is a short to ground on the pin 18 control wire going to the PCM, the PCM gives a ground to the MIL, but it might have a resistor internal to the PCM on that ground control wire. I have never taken one of those PCMs apart. But most circuits that control components inside the PCM will have a resistor to protect the driver for that circuit.
This p0650 code setting criteria states- The control module detects that the commanded state of the MIL driver and the actual state of the control circuit do not match for more than 5 seconds." So, whether the PCM monitors current flow or voltage to determine the MIL state on that control circuit, if that code is still setting the PCM is seeing something it doesn't like, that would explain why your test light didn't go out. LEDs burn out much easier than incandescent light bulbs. It only takes a fraction of a second for LEDs to burn.
There is a TSB on certain lamps not coming on, but it has to do with the fuse that feeds pin 5 which you already tested,
So, focus on the pin 18 wire for a short to ground. Just check it really quick with a meter with the key Off. See if there's continuity to ground.
If there are still all those codes coming back, there is probably a corroded connector somewhere because you haven't lost the Cluster comms completely, it might be an intermittent issue.