Rotating CTRL_Tweak_Chest.002 ,selected on picture, on Y axis affect both front legs and neck all the way to the head. How to make it rotate only front legs, without affecting neck, head rotation.
Changing the "Inherit rot" parameter doesn't work because TGT_Neck.001 bone is part of an IK Chain, so its rot is overwritten by the IK solver.
To have the rig behave as you want you can add a machinary bone, extruded from CTRL_TWEAK_Chest.002, with the same axis orientations, uncheck its "Inherit rot" and its "Deform" options.
Then in edit mode you have to set 3 bones child (keep offset) of this newly created bone (I called it MCH_Head_Base): TGT_Neck.001, DEF_Neck.001 and IK_Head_Target.
I added to the new bone a copy rot constraint, targeting CTRL_TWEAK_Chest.002, so that you can use its influence slider to choose between the old head rotation mode (influence = 1.0) and the new independent one (influence = 0.0).
Some more work it's needed if you want the whole character to rigidly rotate when you rotate the root bone (as it should), but how to it depends by how you want to organize the rig.