"After great pain" uses several metaphors that evoke sufferer's emotionally frozen state.
In line 5, for example, the speaker's description of "mechanical" feet is metaphorical. The speaker is comparing the sufferer's feet to a kind of machine. This comparison highlights the sufferer's lifelessness and lack of emotion; they are robotic, on autopilot.
In line 7, the description of the sufferer walking on “Air, or Ought” is also metaphorical, since the sufferer cannot literally be walking on air or ought. "Ought" can mean “nothing,” “anything,” or “should.” The speaker is illustrating the sufferer’s uncertainty and mental confusion; someone who walks on air, or nothing, is someone who is lost, ungrounded. “Ought” might also imply that the sufferer is mentally ruminating on what they ought to have done to prevent the “great pain.”
The phrase "A Quartz contentment" in line 9 contains an implied comparison between quartz, a hard crystal, and the sufferer's state of numb "contentment." (Note that this metaphor is also part of a larger simile: at the end of line 9, the speaker says that the sufferer's "Quartz contentment" is "like a stone".) By comparing the sufferer's state to quartz, the speaker highlights the sufferer's cold, calm numbness. People in the sufferer's state seem unable to feel anything at all—not grief, joy, nor even pain. They're so numb, in fact, that they even seem to be contented, or at peace, with their current state. At the very least, they don't seem to have the motivation or wherewithal to get out of their state. They are more like a mineral than a human being.
The phrase "Hour of Lead" is also metaphorical. The numbness that comes in the period after a shock, the speaker says, feels as heavy and dull as lead. Lead is an extremely dense metal, and in the 19th century, was commonly used to make bullets and weights. Someone in an "Hour of Lead" feels gray and weighed down by life.
Finally, "letting go" in the final line is a metaphor that compares the physical act of letting go of something to a more figurative surrender. Here, there are several possible layers of metaphor. "Letting go" might refer to dying (letting go of life). It might also mean "letting go" of suffering, either emotional (as in the case of the sufferer) or physical (as in the case of the "Freezing persons"). In any case, “letting go” is a common metaphor that implies some kind of surrender and release.