While some animals see their own reflections and use them to examine parts of their own body that they could not otherwise see.
Animal research has a long history of finding animals exhibiting something that has been touted as a human-only trait; the weight of experience seems to be heading towards the idea that there is no human trait exceptionalism, only a combination of various traits to various degrees. So many traits that someone has posited as the uniquely human trait has subsequently been seen in animals. Maybe one day someone will find something, but thus far the record isn't good.
One could harshly propose that's a failure of imagination (probably shared by almost everyone else, self-included; I introspect in words too), limited by one's own experiences; since you've got language and use it always to introspect, and probably cannot even remember not having language, you cannot conceive of introspecting without it. More so, since it was your field of study; you've immersed yourself in it to a great degree. I wonder if baby humans without language introspect. It seems there is some evidence young humans do [0]. These people say they've seen it in animals, but I'm no expert [1].
I honestly don't know, but I believe that humans are part of a spectrum of animal and I take the opposite assumption to you; that until proven otherwise, we have no singularly unique trait.
[0] https://medicalxpress.com/news/2007-08-toddlers-capable-intr...
I suppose "introspection" is a pretty woolly term, though, and we could disagree about what the bounds of it are. The abstract about "metacognition" in rats is interesting but I think a little broader than what I had in mind.
As an aside on the general conversation at hand, I suspect that the experience of humans is so much based on being a human that we struggle even to think about not being human; that we have so many assumptions we carry about what thinking is and what language is and so on. My favoured example of this is an experiment showing that humans have a special ability for recognising faces, based on giving other primates tests of face recognition. Go humans!
When the test was repeated, some time later, using faces from their own species instead of human faces, it turned out that they were actually also pretty good at it. The original experiment had used human faces to test with, because those were obviously much more distinctive. I suspect, but cannot prove, that we're trying to reason about non-humans from within a prison of human thought and experience and assumption that affects everything.
I never claimed that you can't use noncommittal language to dismiss things for which there is no evidence; I just don't really feel like there is any point.