Is the Theravada system one of direct realism?

Nope. Heres a copy paste of the last time I had to clear this up, lightly edited to make it more applicable here. The previous claim was Theravada is phenomenonism (a form of idealism)so Ive added the word “idealism” here and there for clarity and removed references to the user being responded to:

What emerges from this Abhidhammic doctrine of dhammas
is a critical realism, one which (unlike idealism) recognises
the distinctness of the world from the experiencing subject
yet also distinguishes between those types of entities that
truly exist independently of the cognitive act and those that
owe their being to the act of cognition itself.
-Y. Kunadasa, The Dhamma Theory, page 38

dhamma theory is best described as dhamma realism
-The Theravada Abhidhamma: Inquiry into the Nature of Conditioned Reality
By Y. Karunadasa, chapter 2

This theory ensures that the object of direct and immediate
perception is not an object of mental interpretation but something that is
ultimately real.
-Karunadasa, Y. Buddhist Analysis of Matter, pp. 149.

Thus the Theravādins were able to establish the theory
of direct perception of the external object despite their recognizing the
theory of momentariness.
-Karunadasa, Y. Buddhist Analysis of Matter, page 146

"If we base ourselves on the Pali Nikayas, then we should be compelled to conclude that Buddhism is realistic. There is no explicit denial anywhere of the external world. Nor is there any positive evidence to show that the world is mind-made or simply a projection of subjective thoughts. That Buddhism recognizes the extra-mental existence of matter and the external world is clearly suggested by the texts. Throughout the discourses it is the language of realism that one encounters. The whole Buddhist practical doctrine and discipline, which has the attainment of Nibbana as its final goal, is based on the recognition of the material world and the conscious living beings living therein.
Karunadasa, Y. Buddhist Analysis of Matter, pp. 14, 172

Here is Bhikkhu Bodhi summarizing the abhidhamma position on dhammas:

It is the dhammas alone that possess ultimate reality: determinate existence “from their own side” (sarupato) independent of the minds conceptual processing of the data. Such a conception of the nature of the real seems to be already implicit in the Sutta Pitaka, particularly in the Buddha’s disquisitions on the aggregates, sense bases, elements, dependent arising, etc.,…

Thus by examining the conventional realities with wisdom, we eventually arrive at the objective actualities that lie behind our conceptual constructs. It is these objective actualities – the dhammas, which maintain their intrinsic natures independent of the mind’s constructive functions…

…the commentaries consummate the dhamma theory by supplying the formal definition of dhammas as “things which bear their own intrinsic nature” (attano sabhavam dharenti ti dhamma).

…concretely produced matter…possess intrinsic natures and are thus suitable for contemplation and comprehension by insight.

Great seers who are free from craving declare that Nibbana is an
objective state which is deathless, absolutely endless, unconditioned,
and unsurpassed.
Thus as fourfold the Tathagatas reveal the ultimate realities—
consciousness, mental factors, matter, and Nibbana.
-Bhikkhu Bodhi, Acariya Anuruddha, A Comprehensive Manual of Abhidhamma, pages 3, 15, 26, 235, 260

And here is straight from the abhidhamma:

“All form is that which is…

void of idea,
neither feeling, nor perception, nor synthesis,
disconnected with thought,”
“form exists which is not due to karma having been wrought”

-Dhammasangani 2.2.3

And the Kathavatthu:

Points of Controversy
9.3 Of Matter as Subjective
Controverted Point: Whether matter should be termed subjective or objective.

Theravādin: If that is so, you must also affirm of matter or body, that it has the mental features of “adverting”, ideating, reflecting, co-ordinated application, attending, willing, anticipating, aiming—things which you would, on the contrary, deny of matter.

All, or any of them you can rightly affirm of mental properties, such as contact (mental reaction), feeling, perception, volition, cognition, faith, energy, mindfulness, concentration, understanding, lust, hate, illusion, conceit, erroneous opinion, doubt, mental inertia, distraction, immodesty, indiscretion—all of which you admit as subjective. But matter is not one of these, and therefore such things may not be affirmed of it.

You deny in the case of matter all those mental features—adverting, etc.—but claim for it the term “subjective”, which is really applicable to “contact”, sensation, etc. These, as you admit, do not lack those mental features named.

Uttarāpathaka: But is not matter correlated (as an object)? Of course you assent. Then as correlated it is surely right to apply the term “subjective” to matter, etc. since “object” is one of the twenty-four (causal) relations.

Thus, we can clearly see, Karunadasa confirms, as do the suttas, abhidhamma, etc. that Classical Theravada is a realist system, involving direct realism no less, and that dhammas are mind independent. None of these are anything remotely like, nor compatible with phenomenalism, nor any of the other idealism offshoots.

Compare general objections to phenomenalism:

Criticisms of phenomenalism have tended to be technical. Generally speaking, realists have objected to it on the ground that it is counterintuitive to think of physical objects such as tomatoes as being sets of actual or possible perceptual experiences. Realists argue that one does have such experiences, or under certain circumstances would have them, because there is an object out there that exists independently and is their source. Phenomenalism, they contend, implies that if no perceivers existed, then the world would contain no objects, and that is surely inconsistent both with what ordinary persons believe and with the known scientific fact that all sorts of objects existed in the universe long before there were any perceivers.
-Britannica, Avrum Stroll

And the Buddha himself objecting to the very same ideas that idealists present, and confirming their opposite (objects exist independent of perception):

“If, friends, internally the eye is intact but no external forms come into its range, and there is no corresponding conscious engagement, then there is no manifestation of the corresponding section of consciousness. If internally the eye is intact and external forms come into its range, but there is no corresponding conscious engagement, then there is no manifestation of the corresponding section of consciousness. But when internally the eye is intact and external forms come into its range and there is the corresponding conscious engagement, then there is the manifestation of the corresponding section of consciousness.” “Now there comes a time when the external water element is disturbed. It carries away villages, towns, cities, districts, and countries.”
-MN 28

“Student, suppose there were a man born blind who could not see dark and light forms, who could not see blue, yellow, red, or carmine forms, who could not see what was even and uneven, who could not see the stars or the sun and moon. He might say thus: ‘There are no dark and light forms, and no one who sees dark and light forms; there are no blue, yellow, red, or carmine forms, and no one who sees blue, yellow, red, or carmine forms; there is nothing even and uneven, and no one who sees anything even and uneven; there are no stars and no sun and moon, and no one who sees stars and the sun and moon. I do not know these, I do not see these, therefore these do not exist.’ Speaking thus, student, would he be speaking rightly?”

“No, Master Gotama. There are dark and light forms, and those who see dark and light forms…there are the stars and the sun and moon, and those who see the stars and the sun and moon. Saying, ‘I do not know these, I do not see these, therefore these do not exist,’ he would not be speaking rightly.”

“So too, student, the brahmin Pokkharasāti is blind and visionless.
-MN 99

“And what is it, bhikkhus, that the wise in the world agree upon as existing, of which I too say that it exists? Form that is impermanent, suffering, and subject to change: this the wise in the world agree upon as existing, and I too say that it exists."
-SN 22.94

whether there is an arising of Tathagatas or no arising of Tathagatas, that element still persists, the stableness of the Dhamma, the fixed course of the Dhamma, specific conditionality.
-SN 12.20

. Mind independent matter/form/dhammas cannot be phenomenalism nor idealism.

The dhammas exist even when no one is around to observe them.

For example, per the below, even after a person dies, and consciousness has ceased, their corpse remains as temperature born matter, which can generate all by itself:

But at the time of death, kamma-born material phenomena no
longer arise starting with the stage of presence of the seventeenth
consciousness preceding the death consciousness. Kamma-born
material phenomena that arose earlier occur till the death-moment
and then cease. Following that, the consciousness-born and nutriment-born material phenomena come to cessation. Thereafter,
a continuity of material qualities produced by temperature persists
as long as it can be called a corpse.
-Bodhi, ibid, p 257

Tejo is the element of heat. Cold is also a form of tejo.
Both heat and cold are included in tejo because they possess the power of maturing bodies. Tejo, in other words, is
the vitalizing energy. Preservation and decay are also due
to this element. Unlike the other three essentials of matter,
this element has the power to regenerate matter by itself.
-Narada Thera, A Manual of Abhidhamma p 319

Finally, just to put this nonsense to bed, phenomenalism is a form of idealism, and Buddhism is a form of realism. They are NOT compatible.

Phenomenalism is a form of idealism. Weaker phenomenalism states only that the sense perception can be known to exist, and that it is either meaningless or useless to talk of objects outside of perception. Stronger versions deny that anything exists outside of sense perception.

The dhamma makes it abundantly clear that things absolutely do exist outside of sense perception. This is made undeniably apparent in the quotes above. Thus, the dhamma is realism, not idealism, not phenomenalism, and no amount of the idealist treatment to it can turn it into phenomenalism or whatever your thing is.