"The Spirit of the Almighty gives them understanding" (32:8). What is the Hebrew word behind Spirit here, and where else does it come?

Start with the words. In Hebrew 32:8 has two words where the WEB has spirit: "a spirit in man" is ruach, and "the Spirit of the Almighty" is nishmat Shaddai, from neshamah, which Brown-Driver-Briggs gives as "breath" (tap spirit, Spirit of the Almighty). Elihu uses the same two words together again: "The Spirit of God has made me, and the breath of the Almighty gives me life" (33:4), where breath of the Almighty is the same nishmat Shaddai. Job has both words in one verse too: "the spirit of God is in my nostrils" (27:3), with neshamah earlier in the verse. Elihu has the two words together again in "his spirit and his breath" (34:14). And neshamah is the word of Genesis, where the LORD God "breathed into his nostrils the breath of life" (Genesis 2:7). These verses sit beside 32:8 as parallels. The chapter doesn't say more about what Elihu meant, or whether what he claims for himself is so, and these notes don't decide either.