I think "psychology" for golf is sort of like Spy vs Spy in Mad Magazine.
If you have psychological issues with performing what the world requires, then psychology probably offers some assistance.
But if the issue is how to help the nonconscious do a better job, then, yes, there is stuff to know and work on for enhanced skill performance.
These are mostly perception and movement and focused intentionality. So that's three REAL things to work on to help get the reality of the performance better.
Perception means using accurate physical procedures to generate accurate perceptions; to train the knowledge of what to expect and what to look for and what it means for the putt, and to understand and enhance the way perception forms and shapes and guides the movement's accuracy.
Movement means economy of motion, balance and equilibrium, absence of abstract rules for patterns of movement in favor of objective task accomplishment, eradication of harmful habits, staging the perceptions into the motion, and educating the body for the task accomplishment.
Focused intentionality means treating the mind as that of a moving animal focused solely on the movement task, or accomplishing the goal of the movement.
As to what others preach about the mind knowing this or not being able to tell the difference from that, it's all junk -- just folks talking out of dumbed-down magazine-level knowledge. The brain is multiplex, even if working memory in the conscious mind is limited, and the brain does not need the same sort of abstract / categorical either-or limiting that the conscious mind needs due to its limitations. The brain, in this context, is the 95% or more of the organ that operates on the non-aware or non-conscious level. THAT brain gets good when the intentionality gets focused and simplified and sharpened.
So, putting becomes the task or goal. The goal is to sink the putt by rolling the ball into the hole, and to do so without unduly risking two more putts. If you can have instinctive touch by proper staging of the perceptions in the context of the focused intentionality, then can you also have a stroke that always simply rolls the ball wherever the putter face aims? If so, putting is reduced to reading the putt (and aiming, based upon this read). Then just pull the trigger with good tempo and rhythm and that's the only way to accomplish the goal.
Putting Coach and Theorist