Character rotation jitters when looking around

This line extracts just 2 imaginary components out of a 4-dimensional quaternion:

Vector3 rotation = new Vector3( Quaternion.LookRotation(hit.normal).x, 0, Quaternion.LookRotation(hit.normal).z ); 

In general, it is not safe to extract individual components of a quaternion like this. They're not angles like Euler angle triplets. They're individual components of a point on a unit sphere in 4 dimensions, so they don't really make sense without all 4 components.

Each quaternion component ranges from -1 to 1, so it's not really sensible to use as an angle in degrees here:

transform.eulerAngles = new Vector3(rotation.x,transform.eulerAngles.y,rotation.z); 

It looks like instead you want to do something like this - using a trick I've covered in several past answers:

// Helper function to make an orientation whose local y+ direction matches "exactUp" // and whose local z+ direction points as close as possible to "approximateForward". Quaternion TurretLookRotation(Vector3 approximateForward, Vector3 exactUp) { Quaternion zToUp = Quaternion.LookRotation(exactUp, -approximateForward); Quaternion yToZ = Quaternion.Euler(90, 0, 0); return zToUp * yToZ; } // ... // Start your raycast below your position relative to your current orientation. Vector3 rayStart = Transform.TransformPoint(Vector3.down); if (Physics.Raycast(rayStart, -transform.up, out RaycastHit hit, Mathf.Infinity)) { // Match our vertical orientation to the surface under us, while // preserving our forward facing direction as best that allows. Quaternion matchSurface = TurretLookRotation(transform.forward, hit.normal); // Compute the rotation about our vertical axis according to mouse movement. Quaternion twist = Quaternion.Euler(0, Input.GetAxis("MouseX") * sensitivityX, 0); // Compose these two rotations to get our resulting orientation. transform.rotation = matchSurface * twist; }