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The compressor is still getting warm (as I assume it should) but the radiator up the back of the fridge not at all. I don't know if this confirms what you say about it being seized does it?
Polygon-
The compressor (Black football) would get warm as its being fed electricity for when it's normally running. But it needs the relay to switch contacts over to start the motor first. Otherwise the motor is stationary, drawing current and overheating.
It's still possible that the compressor pump has seized, so the motor can't turn, but way rarer than the PTC/starter giving up.
From your vud, this may have been the Pt number on your comp. Take off the white bit, and get a Pt number for that.
https://www.bekospares.co.uk/fridge-freezer/compressor-jiaxipera-tg1114y-r600a/product.pl?pid=5009704&path=110911&refine=compressor
user69121
The loud click at 8 sec is probably the overload protection tripping as the compressor motor has been drawing current but not running.
It's possible that the compressor is actually seized.
The starting relay lives under the cover on the left side of the compressor. It could be one unit combined with the overload.
Remove cover, unplug wires, pull relay from the 3 pins that connect it to the comp.