Now up front I want to remind people that I’m aware Tolkien hated direct Allegory, like George Lucas he drew on many mythological concepts and motifs, but nothing was meant to be a one to one allegory, even Morgoth’s connection to Satan comes with qualifications (first of which is that it's more of a Paradise Lost perception of Satan then anything The Bible clearly teaches).
Also the development of Sauron as a figure in Tolkien’s Mythology was uniquely complicated. I personally suspect that before Tolkien actually began writing a sequel to The Hobbit, Sauron’s roles in the tale of Beren and Luthien, in the Fall of Numenor and as the Necromancer mentioned in The Hobbit were three completely separate characters. For example in the case of Beren and Luthien the role eventually taken by Sauron was originally just a Werecat type monster. But it’s none of those proto-Saurons I’m comparing to Azazel here, this is specifically about Sauron as The Lord of The Rings.
There are conflicting traditions about Azazel, sometimes that name is just used as another name for Satan, which could very well be the original intent behind it’s use in Leviticus 16. This analysis is mainly about the figure of Azazel as he appears in The Book of Enoch aka First Enoch. The Richard Laurence Translation was published in 1883 and the R.H. Charles translation was published in 1917, so both are books Tolkien could have read at some point.
When I first read the Book of Enoch, I couldn’t help but notice how much Azazel’s role stood out narratively. In the initial list of the leaders of the Grigori/Watchers that fell (chapter 7 verse 9 in the Laurence version and chapter 6 verse 7 in the Charles version) Azazel’s name isn’t included, in either the Ethiopic or Aramaic texts. Yet when Azazel is first mentioned in chapter 8 verse 1 he is suddenly being treated as one of the single most important of them.
Then in chapter 10 verses 4-12 he’s given a uniquely different fate, being buried under rocks in Dudael rather then being chained in the Abyss/Tartarus like the others. I eventually learned some of that uniqueness is a product of how the name is used in Leviticus 16 and traditions derived from that, but it still stands out. If you think you can explain this by just saying Azazel and Samyaza/Shemjaza are different names for the same Angel, the Aramaic text of chapter 8 lists Shemjaza separately as the one who taught Sorcery. And Chapter 9 lists them separately in both versions.
In The Enemy section of The Valaquenta in the published Silmarillion, the only Maia who joined Morgoth singled out for special mention are the Balrogs as a group and Sauron as an individual. One Youtube video I watched on the Balrogs theorized their special status among Morgoth’s followers might be that they were the very first Maia to follow him. Sauron meanwhile came much later, never openly betraying the Valar till after Angband was firmly established. So even the difference between Sauron and the Balrogs echos the difference between Azazel and the Grigori.
But the crux of why I feel this comparison works is what’s said in Chapter 8 Verse 1 of the Book of Enoch.
"And Azâzêl taught men to make swords, and knives, and shields, and breastplates, and made known to them the metals 〈of the earth〉 and the art of working them, and bracelets, and ornaments, and the use of antimony, and the beautifying of the eyelids, and all kinds of costly stones, and all colouring tinctures."That certainly sounds like he’d be a Maia of Aule (as both Sauron and Saruman were) if placed in Tolkien’s Cosmology. In fact it’s tempting to see even the Rings of Power themselves in that verse.
I also can’t help but wonder if Dudael where Azazel met his final doom being traditionally placed East of Jerusalem is echoed in Mordor being East of Gondor.
Another possible mythological influence on Sauron were various pagan gods associated with Blacksmithing and/or Volcanoes. If you were to compare the Valar to the Olympians then Aule would be Hephaestus/Vulcan, yet Sauron ultimately resembles Hephaestus more since Hephaestus was cast down from Olympus. Typhon is a figure in Greek mythology some scholars suspect was originally the same as or an aspect of Hephaestus, one of his birth stories is the same, being borne by Hera in response to the birth of Athena. Also in some versions Typhon is buried beneath Mt Etna a Volcano on Sicily which is also said to be the location of Hephaestus's workshop.
Is it possible to connect Hephaestus/Typhon to Azazel independent of comparing them to a modern literary figure? I think so, like for example winding up buried, and of course Azazel’s status as a craftsman already mentioned above. That the Greeks identified Typhon with Set gives precedence for seeing him as a Desert Storm god. I feel the Book of Enoch definitely developed post Hellenization, it’s mentioning Tartaros is evidence of that. There was a blacksmith god in the Canaanite pantheon, Kothar-wa-Khasis, but he wasn’t cast out like Hephaestus was. So I think the figure of Azazel in the book of Enoch was possibly modeled a bit after Hephaestus and/or Typhon.
So maybe Tolkien likewise consciously or unconsciously made the same connection between them?