What is Auden saying about Achilles’s shield, Achilles’s world (the culture, human nature, the time period he lived in), and Auden’s world? What is the poet’s overall reaction to the piece of art?

W. H. Auden's poem "The Shield of Achilles," first published in 1952, details a description of Achilles's shield, which he used during the Trojan War as shown in Homer's epic poem the Iliad. The poem itself concerns Thetis (Achilles's mother) looking over the shield that the shield-maker Hephaestus is creating. Thetis expects to see images of peace on the shield, but Hephaestus instead crafts images of warfare and destruction, causing much distress to Thetis.
The shield, in Auden's poem, represents the inevitable despair that warfare brings. It depicts scenes of barren wastelands, barbed wire encampments (perhaps a parallel to World War II, which had ended a couple of years prior to the poem's publishing), and soldiers marching to battle. We see in Auden's descriptions of these scenes the devastation that war has brought to the world, and the indifferent public who doesn't speak up about the violence and destruction being committed. Thetis laments these visions, but Hephaestus seemingly has no problem with them; this shows the dichotomy between love and war that the poem discusses throughout.
You could argue that the poem is a commentary on how human nature allows for the repetition of war and violence, even when such actions damage or destroy the world. Hephaestus is not committing the acts he depicts on the shield—but he doesn't protest them either, allowing them to continue both on Achilles's shield and in the world around him. Thetis sees the actions on the shield and is tormented by them, protesting in her cries that her son will receive this representation of violence. The final line of the poem, in which the narrator reminds us that Achilles is destined to die at Troy, cements the theme of the destruction of war and how nobody can stop it once it begins.
This doesn't necessarily apply to any specific timeframe—it could easily describe Auden's reaction to both Achilles's world and his own. The poem was published in 1952, a few years into the Cold War, and the poem may be a response to the rise of totalitarian governments in many parts of the world (most notably, Stalinism). Auden sees the same violence and devastation in his world that he saw in Achilles's and laments that history seems to repeat itself. Auden is the one who describes the deeper meaning in the symbols on the shield, so perhaps it is him—not Thetis—who laments the depiction of war rather than peace.