Compression is decent with no indication of timing chain slip.
Edit: The oil pressure switch output only goes to the instrument cluster. According to the 4th Gen wiring diagrams the instrument cluster communicates with the PCM via the CAN bus. However, the switch activates when the pressure exceeds about 5 psi so the only pressure data available from the PCM would be above or below 5 psi.
Some engines have an oil level sensor and oil temperature sensor in the pan that goes to the message center. I know of one member who had particles from timing chain components block the oil passage to the oil pressure switch. You might try removing the pressure switch and poking something long and slender (stiff wire?) into the passage to see if it is blocked.
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Also, there is a plug on the back of the primary guide that blocks a port (green arrow above) to the passage. If the guide is broken off, oil pressure could be lost thru the open port.
Removing pressure switch is easy, I'll remove and poke the hole this week.
Should i remove the front cover to inspect front guides or is this futile? How likely is that the pump is dead? Is it more likely that the paths are blocked by debris or broken "guide no pressure" condition? Why in the world is it made to lose pressure if guide is broken? (this is crazy design)
There are spring leaves in the primary and balance shaft (usually only AWD vehicles) chain tensioners. The balance shaft chain tensioner is smaller than the primary chain tensioner and its leaves match your description.
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The oil tube pickup screen should prevent larger particles from reaching the pump. It is a big job to remove and reinstall the block cradle to replace the oil pump and more of a job if you have AWD. Unfortunately, the only available port to measure the oil pressure is for the oil pressure switch. I suggest measuring the pressure before removing the block cradle. If the rear cassette has failed, you should pull the engine to replace it. If you post photos of your pieces we may be able to determine what has failed without you having to pull the valve covers to inspect the cassettes.