Code P2088, shuts off and oil light turns on

Hello, with these camshaft actuators, they are both powered up by the brown/yellow wire, which should have power with the Key On or running. The actuator is controlled by its Ground wire which goes back to the Engine computer (ECM). Most of these Ground circuits inside the ECM have a voltage detection circuit coming off the Ground control circuit with a resistor. So, if the actuator is "not" engaged, there will be 12 volts coming through the actuator and down to the ECM, when the cam actuator is activated that 12volts will go to Ground and become 0 volts. So, this might be a power issue to the actuator. The pins on the cam actuator could be loose not making good contact.
So, the first check I would do would be to see if you have 12 volts on the power feed on the brown/yellow wire.
This can also be a camshaft position sensor fault, since you replaced the cam actuator already, we will assume it's a good part. I'll put the code p2088 for other possibilities below.
The third diagram is the camshaft position sensor. At Key On, the yellow/black wire should be the 5-volt Reference, the dark blue/light blue is the Sensor Ground, and the dark blue/grey wire is the Signal Wire to the ECM.
I'm honestly not sure why it wouldn't set cam position sensor codes instead because there would be a fault between the Crankshaft Position and the Camshaft Position, but they list it as a possible fault, and then the Solenoid after, I think you were correct to go after the Solenoid(actuator) since that's what the actual code says. But you may have to replace the cam sensor too.
They are not too clear on which of the two cam sensors is number 1, so you'll have to go by its wire coloring.
Here's Camshaft Position sensor information:

Diagrams 4 and 5 are the Front Camshaft Position sensor's location and removal.
Diagrams 6, 7, 8, are rear Camshaft Position sensor's location and removal. Looks like on the backside to the right if facing the engine. There's an engine hoist hook there so it should be easy to find.
Diagrams 9, 10, are Front cam position sensor's Installation.
Diagrams 11, 12, are Rear cam position sensor's Installation.