Coolant overflow at 190+ degrees F

Long time lurker here. Usually just do a little digging on here to find out the issues and solutions to my gen 2. Unfortunately that car is totaled and I purchased a used gen 3 (2012 v) with 168k miles. After a bit of use it got a check engine light and temporary overheat sign and I am now stumped.

I am in no way an expert mechanic I usually just do small jobs on my own but I was hoping to try and figure this out with the help of this forum.

What I have done is I did the egr and intake manifold clean and changed the intake gasket and throttle body gasket.
I scanned the vehicle with the techstream software and found out the water pump was throwing an error so I changed that and found that the old water pump was definitely messed up. I changed the thermostat.
I also did the spark plugs and oil and filter change.
I flushed out the coolant and had to squeeze all the hoses to get more than one gallon of coolant in. I also removed the temperature sensor to try and get all the air out of the system. Eventually I got about 1.5 gallons of coolant in.
I turned on the vehicle in maintenance mode and all seemed good until about maybe 20ish minutes. The car rpm seemed to drop and then I saw steam coming through the coolant cap opening (cap was not on to let air out) and the coolant level rose and eventually spilled out. This started exactly when the engine rpm seemed to settle/drop.
I tried it again while watching the temperature and noticed it happened around 190 degrees F and the radiator fans did not turn on. ( I have a video of this happening if it helps anyone I can post it.)
To test if the fans worked I turned the AC on and the fans indeed work. I also tested the fan using the battery fan cooling section on techstream and the radiator fan did turn on.

Is there a radiator fan relay that could be out? I know there is 3 fan relays.

Also there are codes that the car throws now and they are P0171, B1503, B2322 and B1585.

Random things I noticed that might help were when the heat is on low the car temperature doesn't go past 186 and the coolant does not overflow.

The dealership filled the car with green coolant not the toyota coolant. I drained it and put the pink cap coolant in.

From what I've read on here these engines overheat and blow gaskets but I have seen no signs (that I know of) of a blown gasket. I will be borrowing a combustion leak tester to make sure it's good. Until then if anyone has any ideas I will greatly appreciate it. Thank you!

 

Temperature is hard to see at the end but when I turn off the heater the temperature goes from 186 to 192.2 and that's when the engine sounds different and the coolant starts to overflow.

 

Will check all those parts you mentioned. If anyone knows I can turn on the "water pump" on techstream and hear a water flow sound.. not sure if that proves that it works but will check if I can feel/see it working. Thanks for the reply.

kept the cap off because that is how I saw it on youtube from some guide videos. will try it the way you mentioned!

thanks for the reply and yes I watched a video on youtube that did it this way but will try what you and and what ChapmanF has mentioned.

i'm silly and completely forgot that about cars... thanks for the reminder!