Check engine light turned on with code P0344?

Hello, have you noticed any running conditions? Or extended cranking while trying to start the engine? I will check on any service info for TSBs and pull up some wiring diagrams for you.

Okay, it is possible for ignition coils that are starting to fail or have high resistance through the spark plug to cause interference when there are voltage spikes. These spikes can get into cam and crankshaft position sensor signal circuits. I have seen that many times, picking up the fault is the more difficult part. If there was an issue with an ignition coil causing this, we would use an oscilloscope to monitor the cam signal and ground wires. And watch for any voltage spikes occur and they can be synced up with ignition coils to determine which coil is causing it. But that is easier said than done.
If you have a scan tool of your own, can you read any live engine data with it? Checking to see if there are any cylinder misfires being detected. But in almost every case if it is a coil, it would take a scope to really find it.
The OEM sensor is listed at about $22, so you could try replacing the sensor and see that helps.
The first diagram below has some possibilities for the code to set. The 2nd is the OEM part number.
I'll pull up the flow chart for that code, but the 2nd step on it is if there are no other codes setting right now, a harness inspection is the next step.

I see there are 4 cam sensors for this vehicle, this one is Bank 1 sensor 1. I assume the sensor 1 is going to be an intake cam, which are the two sensors on the inner section of the cylinder heads in the 3rd diagram. I will see which one is Bank 1 just to verify.

But check the connectors and wiring condition on all 4 just to be sure they are ok. No melted or damaged wires, or connector issues. I will post further info in a few minutes.
The rear cylinder head is Bank 1, as seen in the 5th diagram, so cam sensor Bank 1 sensor 1 is the Intake cam on that rear cylinder head.
You have to remove the air filter tubing to get to the cam sensors, and it looks like they are on the back of the cylinder heads. On the driver side, the inner sensor on the rear head (7th diagram) should be the sensor setting that code.

Yeah, I only see 1 part number. But make sure you buy and OEM sensor, aftermarket sensors can cause more issues, if the code still sets then monitoring the cam sensors signal will be necessary. Something you could try is swapping out the ignition coils from each cylinder head. If a code sets for Bank 2, then that will give you an idea about it being a coil.
After removing the air intake tube, you can access the cam sensors on the back of the cylinder heads. Looking at it from the driver side of the engine compartment, it should be the inner sensor on the rear cylinder head. If accessing the coils is easy, I haven't checked service info yet on it, then you can also check the ignition coil boots for any white marks or burns on them, indicating a coil is arcing outside the cylinder somewhat. I will keep posting further info for you.
Unfortunately, you have to remove the upper intake manifold to get to the back ignition coils, so let's not get into that yet. But you can check the front ignition coils.
This code is a circuit code for that cam sensor,
For 2 wire sensors there is a resistance check you can do, just unplug the sensor and check the resistance across the 2 pins of the sensor, it should be 250-1k Ohms (diagram 4,5).
The 6th diagram is the front Bank 2 ignition coils, you can check them and swap them around. See if that changes anything, at least on the front bank of coils for now.

https://www.2carpros.com/articles/how-to-use-a-voltmeter

These are the rest of the flow chart for that code after the resistance check of cam sensor, this is for checking the wiring harness coming to the sensor.
The first section of the chart has you disconnecting the PCM to check the harness from the sensor to the PCM but check the circuit for any shorts to voltage or shorts to ground first, and then go to the disconnecting the PCM section.

Yeah, there's a bunch of tests you can do with a basic multimeter to at least see if anything stands out. A circuit code is not like a timing correlation code, where the ECM is saying the timing is off. It's detecting something in the circuit or sensor that is not correct.