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You likely have a combustion leak into the cooling system. If you have unexplained coolant loss and pressure tests show no external leaks then it has to be going inside the engine. If there is no coolant in the oil then it has to be burning it.
This will also cause the cooling system to pressurize like you are seeing because of the compression pressures being forced into the cooling system.
What I would recommend now is a block test. This is a kit that comes with a clear vial that you pour a blue liquid in and this is installed over the radiator cap opening. The engine is ran and the liquid turns yellow in the presence of exhaust gases. If the liquid turns yellow then you know for sure that you have a head, headgasket or block issue.