Code P0339?

Both of those codes point to the circuit for the crank sensor, not so much at the sensor itself. Since the code changed after you replaced the sensor I would start at the sensor connector, is it clean inside? No corrosion on the pins? Next follow the harness from the sensor and look for a damaged or broken wire. A common thing is for a wire to rub on a sharp edge and cause coded by shorting, then you move the harness, and that code goes away, but the wire breaks and you get a different code. Now because those were the only codes set, I would look at the dark blue with gray and the brown with light blue wires as the 5-volt feed is shared by other sensors which didn't set any codes for its loss. My normal process is to visually inspect the harness, give the wires a good tug, they can corrode off and fail but still look okay, then move up the harness looking for damage or stretched areas.
Repair the wiring as needed.

I would rule out the sensor and wiring first before thinking internal engine issues.

What testing with a meter did you do? Do you have a scan tool that can read live data? In particular you want to look at the crank signal. A scope would be even better. Trying to eliminate the external items first because tearing things apart and then discovering it was a bad crimp at the PCM connector isn't fun.

Yeah, for critical parts like crank and cam sensors I always use OE. You will need to do a relearn if you change the sensor, but it should run without it. If you can borrow or have a borescope you could use it to look into the hole and inspect the reluctor, but I've only seen one fail and it told the owner it was failing. That is part in the red circle.

Thank you for the follow up. Glad to hear you found the problem.