In the Upanishad itself this is not a free standing prayer but a ritual formula placed in the mouth of a specific priest during a specific act, the pressing of the soma plant, where the text explains each line as accompanying a distinct stage of the pressing and gives an interpretation for why that stage is likened to darkness giving way to light or death giving way to immortality. Removed from that ritual frame, which is how nearly everyone now encounters it, the verse reads as a general prayer for guidance rather than as a running commentary on a Vedic sacrifice, and that removal happened early, since Vedantic teachers have long quoted it detached from the soma context to make a general point about the pursuit of truth. Its modern popularity as a stand alone chant, printed on its own in yoga manuals and recited at interfaith gatherings, is a twentieth century development that owes little to the ritual manual it came from.
The translation dispute is exactly where the philosophy lives. Asat and sat are usually rendered as unreal and real, which suits a Vedantic reading where the verse asks to move from illusion to ultimate truth, but they can equally be rendered as nonbeing and being, which suits an older, more concretely ontological reading closer to the Upanishad's own ritual concerns with mortality and existence rather than with illusion as a philosophical category. A third option, non existent and existent, sidesteps both metaphysical commitments and is preferred by translators wary of importing later Vedantic doctrine into an earlier text, so the choice of English word is itself a choice between reading the verse through Shankara's later non dualism or trying to recover what it meant before that reading was available.