Prius overheating after water pump replacement

My Prius is overheating after changing the water pump, I already changed the temperature sensor, thermostat, 3 fan relays, changed the reservoir cap, replaced the coolant and removed the air bubbles and the car still overheats
Sometimes after driving for 9 hours intermittently (I'm delivery) sometimes after driving after 3 hours.
I've been told it could be the dreaded head gasket but excluding overheating the car doesn't show any of the typical symptoms of a defective head gasket, oil color is dark, car starts soft, coolant level doesn't go down.
I want to thank the members of this forum because you helped me last year to change the water pump without me having any experience with mechanics, unfortunately I put a pump from another brand instead of the original.
I don't know what else to do... I've already taken my car to 2 different mechanics and I talk on the phone with 2 more mechanic friends and I can never solve this problem, as I depend on my car to work and earn my money I'm desperate not knowing what to do, If anyone can help me I will be eternally grateful.
Prius 2010 - 180k miles

 

I will describe the facts in more detail to facilitate understanding.

First the yellow engine light came on and after 6 minutes the yellow triangle came on making the car stop completely...the car was towed.

The other day my friend reset the code for me to do a test with the car (P261C), but when I was 2 miles from home the yellow triangle came back and I didn't want to wait for the tow truck I reset the code continuously to get home (maybe this damaged the car).
After the mechanic changed the water pump the car showed a red engine light and after driving for 5 minutes the yellow triangle came back again I reset the error code to be able to go home (3 miles).

The pump was replaced again with another one and after working for 8 hours the engine overheat light came on on the highway, some coolant had been expelled from the cap.

*When the light came on I took the first exit of the highway and the overheat light went out, after opening the hood the fans were not working at the moment (the car overheated several other times and I never saw the fan working), but when I turn it on the air conditioner I see the fan working normally, I already saw it working in stage 2 which is faster...I replaced the 3 relays of the fans

The temperature sensor was changed and when I stopped the car to make a delivery I noticed a pulsation noise coming from the engine, it seemed to be the coolant moving through the hose in pulses (I had heard this noise last time), a little coolant was expelled through the lid without even the engine overheat light appears (fans were not working), after 5 minutes the light came on.

The thermostat was changed and this time after just 20 minutes driving the light came on (fan not working and some coolant splashed through the lid)

The reservoir lid was changed and the light came back on, I took the car to another mechanic who used a machine to remove the possible air bubbles from the coolant and yesterday the light came on but this time when opening the hood the engine was cold the liquid did not it was boiling like the other times.

Honestly I don't know what else to do...I've been told to sell my car, but I would never sell it hiding this problem because it can cause serious damage to an unsuspecting buyer, and I wouldn't be able to buy another car for the probable amount paid.

 

Update- Something I noticed, every time the car overheats the fan is never running, but mysteriously when I turn on the A/C and the engine is hot the fan turns on

 

The code that I was clearing were always the same P261C, after that the water pump was replaced by another one and the problem with overheating started to appear

 

After changing the water pump, the engine red light appeared…after I had driven for 20 minutes the yellow triangle came on…the water pump was replaced again and no light came on except for the overheating light when I drive much…no error code also appeared at this time

 

Another thing I noticed…measuring the ECT temperature (I believe it's the coolant), normally the temperature goes up to 90 °C and then drops quickly to 87 (I believe it's the cooling system kicking in (water pump and the fans), but sometimes for some reason that I don't know in one of my tests even with the car stopped but the engine running only to recharge the battery the temperature went from 90°C and rose to more than 110°C without me moving the car, and right after the engine overheat light came on, I stopped the car quickly and the coolant was not moving in the reservoir that means the water pump was not working at this point and the fans were also stopped, it seems to me to be an intermittent problem where sometimes the water pump works and sometimes it doesn't

 

I improvised the scanner to measure the temperature of the coolant in real time, so I prevent the engine from overheating by stopping the car.

One more additional detail, the thermostat was changed 2 times in less than 2 weeks and even so the temperature of the tube that comes out of the thermostat is always cold to the touch, is it a problem with the water pump that has just been changed?

 

My scanner tool is simple I can't monitor the water pump RPM...but something that intrigues me is the hose that goes out of the thermostat and goes into the radiator is always cold even after driving a lot and being a recently changed thermostat

 

I took it to a mechanic and he used a machine to take the air out and charged me 100 bucks and the problem continued, then I drained all the coolant and put it back in leaving the car in maintenance mode for more than 20 minutes and the problem persists.

 

The mechanics want to do the head gasket, but I'm not sure if it's really the head gasket.
The coolant level never went down, the engine oil is dark and the combustion engine works normally during start-up
Is there a possibility that the head gasket is having problems even without showing symptoms? (overheat only)
Every new mechanic I take my car wants to change again the same parts that the other mechanics changed.

 

A year ago I had installed a non-OEM pump and the problem came back, but now I switched to an OEM pump but it seems that it stops working when the engine warms up (I'm not sure, but when the coolant temperature exceeds 95 degrees celsius the temperature rises quickly)

 

It started to heat up after changing the water pump, I took it to a mechanic who used a special machine to remove the air bubbles and the problem persisted.

The thermostat was changed 2x in less than 2 weeks (I had said the hose was cold but I believe I was monitoring the wrong hose)
About techstream I took my car to a mechanic specialist in hybrid cars and he has this tool but he couldn't find any problem.