2006 coolant running out quickly

Jjb0800 wrote: ↑Fri Feb 25, 2022 4:24 pm Headgasket was already replaced cost me £300 when I bought the car. After that I'm not sure if my faulty thermostat caused my car to overheat has affected the hg.

You can do the head gasket test (from here - eBay) to check the head gasket has not failed again or been fitted incorrectly. It's a test you can do yourself and will take a lot of the guessing out of it.

Jjb0800 wrote: ↑Fri Feb 25, 2022 4:24 pm Headgasket was already replaced cost me £300 when I bought the car. After that I'm not sure if my faulty thermostat caused my car to overheat has affected the hg.

You would see by the temperature gauge if the engine had over heated.
Tu3 has "wet liners". The pistons run up and down in steel tubes "floating" in the engine coolant. Lots of possible failure modes there.
There are a number of ways the head gasket can fail but corrosion, warpage or cracks in the head are also possible causes for coolant loss.
If you are using an antifreeze coolant in your system, the coloured dye or a powdery residue should be visible on the outside of the engine if it's leaking that way. If you are just using water you might not find the leak.
If the coolant is going into the cylinders there will be excessive amounts of steam coming out the tail pipe and the engine will be rough at idle. Fuel trims will be shot too.