Sankatasana is described in the second lesson of the Gheranda Samhita: the left foot is set on the ground, the right leg is wound around it, and the hands rest on the knees. Sankata means narrow, contracted, straitened or difficult, and the name is for the winding in of the legs rather than for any claim about the practitioner's experience.
The word has a second life in Sanskrit devotional usage, where sankata is trouble or distress, the thing a deity is asked to remove. Sankatamochana, the remover of difficulties, is a widely used title of Hanuman. The manuals do not invoke that sense and the atlas does not attach it to the posture, but readers meeting the word elsewhere will meet it in that register more often than in this one.
The Hatha Yoga Pradipika does not carry the posture. It belongs to the group of standing and half standing forms that the later manual adds, a group that also includes the tree and the raised posture, and among them sankatasana is described with the most mechanical precision: which foot is down, which leg winds, where the hands go. Standing forms are rare enough in the classical corpus that each one is worth marking, because the modern repertoire is built largely on standing work that these texts do not contain.