yes that is the part you need, but there are two style. A style with a retaining bracket and a still without (as pictured) You'd need to confirm before ordering.
Opinions on the long oil change interval aside. I'd be pushing for the dealer to clean the current units in an ultrasonic bath especially given the history of the engine.
I'd be surprised if they don't come good after a clean. Re the phasers the car will report them as an issue if the car commands a change in Cam position but it doesn't happen.
This can be because the phaser is actually stuffed or because it's not getting the oil required to move it due to a faulty/blocked solenoid.
Holding the pedal flat to the floor and cranking the car will reset the phasers. So i'd push them to clean the solenoids, reset the phaser as described and then let it run.
The phaser have physical limits in place so the cam angle cannot move to the point engine damage can occur.