So @susanontherocks, as someone who nearly dedicated my life to studying the history of porcelain, I love this question!
I'd argue that ceramics are so important for humanity that they're often connected directly to creator gods more generally. Even when there aren't Kiln-Gods specifically in some mythologies/cultures, that gap is often filled less directly by having Gods-as-Potters (in place of, or in addition to Kiln Gods).
actually for an example I'm familiar with as a Jew, this is definitely a running theme in the Hebrew bible! It's one of those things that I think a lot of people haven't thought about, or don't realize when they read in translation but it's sort of everywhere and enough that I would say YHWH is - if not specifically a god of pottery, then definitely a God frequently titled as a potter!
The earliest positioning of YHWH as a creator-potter is Genesis 2:7, where YHWH forms the first human from the "dust (clay) of the earth." The verb used is וַיִּיצֶר֩ which...literally is the word for forming/molding something out of clay as a potter! And that is hammered home by the first human being 'adam (the word for ruddy red, like clay) made from ha-adamah (the soil). In psalms, the first time the word "golem" is used is as "golmi" ("my golem,") which is referring to the unfinished human before god's eyes as like, raw material (which is what golem means and why Golems are made of clay!).
But now, O ETERNAL One, You are our Father;
We are the clay, and You are the Potter,
We are all the work of Your hands.
Plus in Jeremiah 18:6 "just like clay in the hands of the potter..." And again in Isaiah 45:9 which compares YHWH to a potter and humans to a potsherd of earth.
Job 10:9 refers to YHWH fashioning him from clay, echoed again in Job 30:19. And in Job 33:6, Job makes an argument for the basic equality of humanity, again comparing God to a ceramicist: "You and I are the same before God; I too was nipped from clay."
Isaiah 41:25 implies that the kinds of power that YHWH can grant those who invoke their name can "trample rulers like mud, like a potter treading clay."
This parallels with your example of Khnum, even with the implication that unborn humans are first formed in clay by the deity before they end up like...in the womb).
Other creator deities as potters would be like:
Enki making humans of blood and clay. Also sumerian mythology is the mother goddess Ninhursag making humans from clay.
Some Prometheus myths involve him making humans from water/earth (or making a statue of Athena from clay that is then given life from a stolen sunbeam)
The mother goddess Nüwa forming humans out of the mud of the Yellow River
Zoroastrian creator deity Ahura Mazda forms the primordial human from clay
The Yoruba Orisha Obatala makes humans from clay and is the god of the earth.
There's a billion more - I think loads of creator gods are potter-Gods, but maybe aren't necessarily the same as Kiln-Gods although arguably a potter might have historically valued a potter-God all the same, since ceramics and pottery are often directly tied to the mythology of the most fundamental creation of humanity. These also sometimes overlap in the domain of fire or lightning gods. The Italian Renaissance artist Picolpasso does describe christian ceramicists praying specifically before lighting the fires of a kiln.
Also related: there ARE demons of pottery in Greek myth! The Daimones Keramikoi: Suntribos (the Shatterer), Smaragos (the Smasher), Asbetos (Charrer), Sabaktes (Destroyer) and Omodamos (Crudebake).
Someone wrote a dissertation on the influence of Chinese Kiln-Gods on American ceramicist rituals: Pathways of Transmission: Investigating the Influence of Chinese Kiln God Worship and Mythology on Kiln God Concepts and Rituals as Observed by American Ceramists by Dr. Martie Geiger-Ho, but I'm not familiar with them or their work, tbh.
I have read William Fairchild's writing before though, and he has an article from the 60's which argues that Japanese myths replaced clay with metal in relation to deities of fire and lightning, which could be related/interesting.
And in Chinese, a pottery/kiln God is called 窑神 (Yaoshen, literally Kiln God). I'm having trouble verifying specifics with simple online searches and it would take me a looonggg time to go through all my book-PDFs but I suspect there's a fair amount of overlap there with Chinese folk religion, and especially daoism since there's a concept of the internal furnace, and alchemical concepts often overlap with ceramics in various ways.
