Prius still overheating even after spending $1000 at the shop

y'all experienced DIYer out there. I am helping a friend with his 246k mile 2015 Prius overheating issue. I really need some guidance to help sort it out.

Background: a couple of months ago the prius temp warning light came on. My friend found the water resevoir was nearly emply with just a bit of coolant left. He filled it up with 50/50 Preston (compatible with all Japanese imports) coolant. I am pretty sure he did not know he needed to bleed the air. Anyhow, he continued to drive it to work (40 miles each way on highway) for about half a month until the overheating turned. At this point he took it to a local shop. They replaced the coolant recovery tank and cap (even though it was not leaking), and thermostat/housing assembly. That didn't fix the issue but they charged him $1057.97 any way.

Here is their diagnoistics: "There is a lof of staining and buildup on and below surge tank. start with surge tank and cap. Fans work and everything else seems normal. A TSTAT due to it being over heated..."
Post repair notes: " While attempting to fill the cooling system, tech found hat the heater core hoses are clogged w/ crystalized gel/coolant. This is cuased by not using the proper coolant. The only way to repair this is to replace the entire cooling system and can not be flushed out. Recommend dealer for repairs."

Here is what I observed and tried after he came to me:
1. checked his coolant bottles to make sure the coolant is at least compatible, drove the car for 2-3 miles to cause the temperature warning light to come on. Noticing an engine light also came on briefly after the temp light, I plugged in my Bluedriver OBD2 and saw that Engine coolant temperature went over 220F and hovered slightly up and down there while idling. Meanwhile, all the fans were on and you would hear this clicking sound (like opening a relay) every few seconds and would see coolant rushing into the revoery tank through the top hose after each click. The tank felt very hot to the touch. The only code I picked up was a P0177 "Engine Coolant Temperature Sensor 1 Circuit Low". I didn't believe the tech story about the heater core since they didn't even charge for labor to tear into the heater core hoses. But I did verify that there was no heat when I turned the heater.

2. The second time, I decided to put the car in Maintenance and burped the system. At first the temperature seemed hovered right round 220F. I turned on the heater on high and there was warm air finally (but not hot). Then the temperature started to shot up and hot coolant squirted out of the funnel in the recovery tank opening. It kept going up to 338 or 339 before I shut the car down. Tried a couple more times, same result, and no more heater. In fact, I felt it got worse when I turned on the heater.

3. Next, I decided to flush the heater core with a garden hose. The coolant came out as clean and pink as it could be with very little debris. I back flushed it first then flushed at the normal direction, draining sever big buckets of water. I finished the flush with the 50/50 premixed coolant. By the way, when I first disconnected the heater core hose from the outlet, no coolant came out and the inside of the rubber hose was completely dry. I tried to burp the system again but same thing happened. I suspected there might be huge air pockets but the temp shot up so fast in maintenace mode and coolant spilled like crazy I just could not continue to burp. I will try to append a video on that.

My thoughts:
1. This is caused by no circulation of coolant. I initially didn't suspect the water pump being the case because they told me two or three year ago they had an overheating case, had to tow the car to a shop, and they fixed it with a new water pump. Now that I thought over, it's most likely the water pump, barring a defective new thermostat or the coolant temperature sensor.
2. But from what I read in this forum, the coolant temperature sensor can throw a "short circuit" code like that if the temperature gets up to 248F (or something like that). Besides, I was monitor the temperature changes on my scanner the whole time and didn't see anything wrong. I would think the temp display would be dead or wrong if the coolant temperature sensor is bad. Am I correct?
3. About the only thing left in this is the radiator. I forgot to feel the temperature difference on the low and high coolant hoses going into the radiator.

Questions:
1. what do you think of the situation and my though process?
2. Is there an easy way to figure out if the water pump isn't working without taking it out? I did not notice any strange noise coming from down there. I guess I can try to feel the inlet and outlet hoses but I will need to remove the air intake box to reach down there.

Sorry for the lengthy description. I want to provide a complete picture without too much going back and forth in the thread. Thank you so much in advance for your valueable input!

 

For the short video mentioned above, I couldn't imbed this youtube link because I don't meet minimal requirements yet. So if you are interested, please search youtube for this exact phrase "2015 prius overheating daniel wang". It's 10 second shorts. Thanks!

 

I don't believe this garage told the truth in the report. To get to the heater core hoses you have to take the windshield wiper motors and the cowl off. They did not charge any labor about it (but they charge well over $400 for the recovery tank!). LIke I said, when I flushed the heater core, clear pink water came right out of the heater core. There was no clogging, as I had expected.
That said, I do think it's a good idea to flush the radiator and check the thermostat (shop replaced it). I will do the compression and leak down tests after I figure out the circulation issue. Thanks for the suggestion!

 

He actually bought it new. The miles are all highway driving. According to him, the car had been driving fine until the recent overheating. He said he did not continue to drive when the overheating light came on. And he only added the coolant when he found it extremely low in the tank. I think the coolant got too hot and spilled out of the cap. There is not leak. He did replace the water pump once 2-3 years ago due to overheat and had had no issues until now. So most likely the head gasket is still okay. And there is no code other than P0117. My focus now is to fix the overheat issue and go from there. Thanks!

 

He's the one owner of this car. The only thing he said he added was to refill the coolant recovery tank when he first overheated two months ago. He drove for another two weeks on the highway to work with no issues (35 minutes each way) until it overheated again. He has not really driven it other than taking it to the garage a few miles away and back. The shop replaced the tank, cap, and thermostat. My guess is that the water pump gave up again (it did 2-3 years ago). I am hoping the rest of the car is still okay. I am going to tear into the water pump tonight. Thanks.

 

You are right, Sir. I meant 238 or 239 F. Thank you for the explanation of the heater and egr cooler secondary circuits. I knew it didn't make any sense for the heater core clogging, if any, to cause circulation problem of the main cooling system. I will find out if the pump is an OE or not tomorrow. Regarding the HG, I didn't really check because they never had performance issues and the car seemed to be fine in the little test drives I had. I pretty much stopped as soon as overheating started. I only kept the engine running as long as I obtained some evidence.