What is the term that represents knowing, and not knowing what it is like not to know?

Solution 1:

It's more biology than linguistics but it sounds like learned or acquired reflex.

a reflex which is learned through practice or repetition and may involve both a far more complicated set of triggering stimuli and a far more complicated pattern of motor response,

e.g., the reflexive motor actions produced after one has learned to ride a bicycle or drive a car; most such reflexes are somatic because they involve complex response patterns from skeletal muscles.

There is also a psychological term: Unconscious competence

The individual has had so much refining practice with a skill that he or she does not really need to think about what to do. It has become "second nature" and can be performed with very low frequency of errors.

Because the skill is not occupying much of the individual’s conscious thoughts, it can often be performed while executing another task. The individual has become so comfortable with the skill she/he will often be able to teach it to others.

Based on your edits, it is related with Curse of knowledge also:

The curse of knowledge is a cognitive bias according to which better-informed people find it extremely difficult to think about problems from the perspective of lesser-informed people.

Solution 2:

The scientist and philosopher Michael Polanyi called this personal knowledge¹ or tacit knowing².

He argued that the mastery of skills—not merely crafts and physical skills, but intellectual and artistic disciplines such as scientific research and conoisseurship—depends on acquiring an internal, appropriated knowledge of rules which cannot be specified.

    The skilful use of a tool actually identifies it to an important extent with our own body. The rower pulling an oar feels its blade tearing the water; when using a paper-knife we feel its edge cutting the pages. The actual impact of the tool on our palm and fingers is unspecifiable in the same sense in which the muscular acts composing a skilful performance are unspecifiable; we are aware of them in terms of the action our tool performs on its object, that is, within the comprehensive entity into which we integrate the effective use of a tool. The same is true of a probe used for exploring a cavity or a stick by which a blind man feels his way. The impact made by a probe or a stick on our fingers is felt at the tip of the probe or stick, where it hits an object outside, and in this sense the probe or stick is integrated to our fingers that grasp it.
    A feature of great importance enters here in the way the assimilation of an instrument to our body is achieved gradually by learning to use the instrument intelligently. When first groping our way blindfold with a stick, we feel it jerking against our hand. But as we learn to understand these jerks in terms of the impacts of the stick against outer objects, we begin to feel the end of the stick knocking at these objects. Thus the jerks against our hand, when integrated to our purpose, undergo (along with a change in quality) a transposition in space. We see here that when a particular is integrated into a comprehensive entity it may acquire a meaning which is sensed at some distance from the original position of the particular, at which it had been previously experienced in itself, meaninglessly. Other examples of such shifts, directed likewise away from our body, will be met in the use of language and the act of visual perception.³

¹ Polanyi, Personal Knowledge: Towards a Post-Critical Philosophy, University of Chicago Press, 1958.
² Polanyi, The Tacit Dimension, London: Routledge, 1966.
³ Polanyi, “Tacit Knowing: Its Bearing on Some Problems of Philosophy”, Reviews of Modern Physics, 34 (4), 1962, 603-4.

Solution 3:

Metacognition is the ability to reason about one’s own reasoning or knowledge, including the understanding of one’s own limitations (or lack thereof).

The term metacognition literally means cognition about cognition, or more informally, thinking about thinking. Flavell defined metacognition as knowledge about cognition and control of cognition. For example, I am engaging in metacognition if I notice that I am having more trouble learning A than B; [or] if it strikes me that I should double check C before accepting it as fact.

There’s a common kind of metacognition failure called the Dunning-Kruger effect which is loosely connected to the sense that you’re talking about. It’s not directly on point – in some ways, it’s the opposite of what you’re looking for – but you may find it helpful.