I am struggling to understand what causes this flip and looking for some advice on how to correct it.
Quaternion newRotation = Quaternion.LookRotation(target.transform.position
- transform.position, Vector2.right);
newRotation.x = 0;
newRotation.y = 0;
target.transform.rotation = Quaternion.Slerp(target.transform.rotation, newRotation, Time.deltaTime * 8);
Here, everything is as expected.

Here, the angle flips.

Thanks for reading.
The newRotation.y is not the representation of rotation of a gameobject in degree. I think you should work with newRotation.eulerAngles.
it will be like this:
newRotation.eulerAngles = new Vector3(0,0,newRotation.eularAngles.z);
The cause of the flip is most likely because you are changing directly the coordinates of a Quaternion,
and these coordinates, even though they are related to a rotation of an object, they are not directly angle values. Therefore the following lines:
newRotation.x = 0;
newRotation.y = 0;
are not successfully doing what you are expecting, which I guess is to zero out rotations around the axis x and y, while looking at your target. One way you can achieve this “look-at”
functionality restricted to a plane, is to use the Vector3.ProjectOnPlane method :
using UnityEngine;
using System.Collections;
public class LookAtOnPlaneTest : MonoBehaviour {
public Transform target;
void Update () {
//change as needed (here rotate around y axis)
Vector3 rotationAxis = Vector3.up;
//project direction to target -> into the rotation plane
Vector3 projDirToTarget = Vector3.ProjectOnPlane (target.position - transform.position, rotationAxis);
//get the rotation for looking into the projected direction
Quaternion newRotation = Quaternion.LookRotation (projDirToTarget, rotationAxis);
//animate rotation of character to the new rotation
transform.rotation = Quaternion.Slerp (transform.rotation, newRotation, Time.deltaTime);
}
}
the ProjectOnPlane method will do what you want of projecting the dirToTarget into the plane with normal equal to rotationAxis, and you look-at that projected vector.