Yellow sludge like oil in my water bottle. Thermostat

There are a few possibilities;

The fluid in overflow could be engine oil and the head gasket is bad. Check Engine oil for a white, milky substance which would further confirm this diagnosis.

The transmission cooler is leaking. It is integrated into radiator and can leak a red or light red fluid into the anti-freeze. Transmission fluid would have red, milky fluid in it if this is the case.

The thermostat on the 1.4 16v engine accommodates both oil and water. Failure of the gasket or housing can cause the two to mix.

The thermostat is isolated in the cooling system. It runs around 15 PSI while oil pressure runs around 60-80PSI. So it takes a heavily torqued gasket to seal out the oil from the thermostat.

The thermostat gasket is just to keep anti-freeze from leaking out of engine.
In the head and water jacket passages of the engine, are areas where the 2 fluid circuits come close to each other. If a head gasket fails near the oil circuit it tends to either leak into the anti-freeze circuit, which can over-pressurize it and you may notice extra coolant in the overflow, or in the cylinder where it will make the exhaust have a burnt oil smell. If the Anti-freeze circuit leaks it leaks down into the oil pan by way of return passages that are under residual pressure.

If anti-freeze gets in the cylinder the exhaust smells sweet like anti-freeze and is generally white.

So, I think from what you are desribing, and the reason I mention the above, is that the only way to have cross contamination is to have a crack in the engine block or to have a bad head gasket. The thermostat seal has nothing to do with sealing either fluid circuit from each other.