When did we first start envisioning extraterrestrials as other animals/biological things, rather than angels, demons, etc?

While I am not claiming that this is a definitive answer, the philosopher Immanual Kant develops a distinction between Humans, Angels and what he calls "Other Beings." This is something that is stretched between multiple works, but one footnote example of this reads:

“The role of the human being is thus very artificial. How it is with the inhabitants of other planets and their nature, we do not know; if, however we discharge well this commission of nature, then we can well flatter ourselves that among our neighbors in the cosmic edifice we may assert no mean rank. Perhaps among them every individual might fully attain his vocation in his lifetime. With us it is otherwise; only the species can hope for this.”

This is from his Idea for a Universal History which is published in 1784.

He also develops this in Universal History and Theory of the Heavens (Published earlier in 1755) where he not only makes an explicit distinction between angels, who have "holy wills" and other beings who has wills in the same way that humans have wills, but he provides some examples of these beings odd assertions about these inhabitants of other planets (that their fundamental dispositions are based on the amount of heat-based energy their planet receives from the sun).

I don't think Kant is the first person to make this Angel/Alien distinction but he does develop it, if you look for it, and he does make this idea fit in with his overall moral theory.

(This is all based on a rather pedantic seminar paper I wrote a while ago)

This is complicated, and in part because the question presupposes an either/or - extraterrestrials are liminal creatures, neither this nor that, or sometimes both this AND that.

For example, possibly the oldest recorded UFO sighting is in Ezekiel 1, the "wheels" that descend from the sky in flames and visit the prophet. They're explicitly said to be angelic (they're in the Bible after all!) but are also described in terms of "living beings" who are kind of crewing the jeweled gyroscopes.

The whole encounter is not too long to read and thoroughly weird from a modern perspective (and, indeed, from an ancient one too).

This encounter (and a similar one in Daniel) is why there’s a ranking of angels called “wheels” or ophanim. In other words, the things that we modern readers might be inclined to see as “ships,” were, for a long time, thought of as entities in themselves. The ophanim carry the cherubim, somehow, or escort them – they’re two kinds of angels seen together. Possibly. (Liminality again, get it?)

OK, so that’s a biblical thing that might be interpreted as an extraterrestrial encounter nowadays, and that illustrates the bizarre quality of angels as sort of embodied and sort of not, and sort of machine-like as well as sort of spiritual. That’s the essential quality of these encounters – they violate the categories.

Fast forward from that, encounters written down in the medieval period tend to be described in explicitly spiritual terms – the one that comes to mind is the Early Modern “Mowing Devil” blamed for one of the first crop circles. Bright lights, physical phenomena, an oath to the devil… is it a spiritual encounter or a physical one? Well, it must be the devil… right?

Then, around the dawn of the Industrial Age, there were the mystery airships, which were machines crewed by humans who might have claimed to come from Mars… or to be “the lost tribe of Israel” (possibly from inside the Hollow Earth… which gets into a whole other category of paranormal belief).

The term “flying saucer” was coined in the late 1940s about what appeared to be physical craft, albeit highly reflective (similar “foo fighter” sightings during WWII were less physical – usually attributed to electromagnetic phenomena like St. Elmo’s fire or ball lightning, little blobs of energy zipping around the sky).

By the 1970s, though, a kind of narrative was emerging with the pilots of the craft taking a kind of angelic or demonic role. Contactees like Billy Meier assured people that the UFO pilots were looking out for our future on Earth… like guardian angels. On the other hand, abductees following pattern of the Barney and Betty Hill case were somewhat less sanguine about alien overseers… which developed into the Serpo mythos (and I'm using “mythos” here just to mean a body of beliefs, not as a comment on its facticity): the idea that the government had made a secret deal with grey aliens, that they were breeding human-alien hybrids, that the New World Order the first President Bush talked about was going to be controlled by technologically advanced aliens who somehow existed outside our conception of time. That’s a weird thing to turn over in your head.

And once you get the New World Order mixed in, you get the threat of End Times prophecy and the Beast of Revelation and all that fun stuff bubbling up around the edges, as in this release – go about three quarters down the page. The aliens will outlaw Christianity? Really?

If you’re interested in plunging into the nature of extraterrestrials as sort of embodied and sort of not, check out Patrick Harpur’s Daimonic Reality (a really fun read), and George Hansen’s The Trickster and the Paranormal, a very thorough examination of the weirdness and liminality around this stuff.

John Keel’s The Mothman Prophecies is also about much the same thing – the Mothman has many of the same qualities as extraterrestrials, being a thing that is seen and interacted with but also a kind of omen or spiritual being, and has possibly-not-human attendants or co-travelers (the Mothman sightings include some of the most developed Men In Black encounters on record).