Is "space" directly accessible to the senses?
It is not because it is the absence of sensation. Much as one can sense small quantity through subitizing, one can also be keenly aware that nothing is present, so too can one see motion and length or feel force, but be keenly aware that none occurs or exists. Is it true to say that the property of lacking sensation is itself a sensation?
No, because if one accepts the law of non-contradiction one cannot accept these two propositions: "space is not sensing" and "space is sensing". Hence, the simplest dichotomy for apprehension is the language of the mind-body duality, it is a conception (mind, not sensation) characterized by the absence of perception (body, sensation). This is why it is considered an abstraction and not a physical thing.
See this SE post for more details about how the concept is computed neurally
Whether you are talking about "void" discussed in Antiquity, "absolute space" during the 17th and 18th centuries, or " relativistic space-time" of the last century, the notion is essentially the same. A space or discontinuity in matter is what a pit is to the ground, emptiness, and the more sophisticated the philosopher, the more complex the constructed concept.
According to the SEP on Newton's Views on Space, Time, and Motion:
The most important question shaping 17th-century views on the nature of space, time and motion is whether or not a true void or vacuum is possible, i.e., a place devoid of body of any sort (including rarified substances such as air). Ancient atomism, dating back at least to the pre-Socratic philosopher Democritus (5th century, B. C.), held that not only is such possible, but in fact actually exists among the interstices of the smallest, indivisible parts of matter and extends without bound infinitely. Following Plato, Aristotle rejected the possibility of a void, claiming that, by definition, a void is nothing, and what is nothing cannot exist.
In modern physics, space is often conceptualized either as a discontinuity of atoms and other particles or as a field which is continuous everywhere echoing the ancient debate.