I understand you want to rotate in Z, but LookAtRotation will always point the X vector at the target.
If I want my turret to point the gun at the target, the X vector must be along the gun
Notice, I have my gun ( cylinder ) attached to the turret cube, so I just need to move the turret. The X of the turret is facing along the gun
Yours is like this
so ‘lookat’ will point the side of the turret at the target.