The first thing to keep in mind is that sorcery/witchcraft/etc were a normal and expected part of Aztec life. Like most pre-modern societies, there was not a hard distinction between "natural" and "supernatural" causation of events. Magic was a natural force, to be used and utilized.

In that vein, the most succinct description of a "witch/bruja" comes from Sahagún's Historia general de los Cosas de Nueva España. The selection is actually describing a "bad [female] physician]" (amo qualli ticitl):

She bewitches -- a sorceress, a person of sorcery, a possessed one. She makes one drink potions, kills people with medications, causes them to worsen, endangers them, increases sickness, makes them sick, kills them. She deceives people, ridicules them, seduces them, perverts them, bewitches them, blows [evil] upon them, removes and object from them, sees their fate in the water, reads their fate with cords, casts lots with grains of maize, draws worms from their teeth. She draws paper, flint, obsidian worms from them; she removes these from them. She deceives them, perverts them, makes them believe.

From this we can make a couple of inferences. The first is that "a sorceress" (naoale in the text, but nahualli in the modern orthography) causes harm to people, physical and psychological harm. The second is she is a liar, a deceiver (teixcuepani). She is using her gifts and skills to manipulate people.

The clearest example of this is the bit about "draw[ing] worms from their teeth." There was the idea that a "tooth worm" caused cavities. The bad female physician in this case is being accused of drawing out false worms made of paper, flint, or obsidian, in order to deceive her patients into thinking she had drawn out the worm. The fact that there was no such worm is irrelevant, since, emically, there was.

Indeed, if we look at the most basic Nahuatl word for a witch, naoalli/nahualli, we can again see a heavy emphasis on deception and manipulation. The "bad sorcerer" is described in Sahagún as:

a doer [of evil], an enchanter. He bewitches women; he deranges them, deludes people; he casts spells over them; he charms them; he enchants them; he causes them to be possessed. He deceives people; he confounds them.

This description is part of a chapter generally covering "enchanters, sorcerers, and magicians" which also includes soothsayers and, amusingly, attorneys and solicitors/salesmen. There could be both good and bad examples of all these professions, but the idea that a bad person would use their talents to manipulate others rather than putting in the hard work is constant throughout. A good solicitor, for example, "goes without his food, without his sleep" and yet still "solicits with empathy." Whereas a bad solicitor "blinds one, distracts one, lulls one to sleep in order to rob him; who destroys by sorcery; removes by stealth; accepts bribes."

The second thing to keep in mind is that there were an astonishingly large array of types of "witches", and that like the "bruja/brujo" term that Spanish uses, the role was not necessarily gendered. Lopez Austin published a well regarded paper in 1967 about the "40 types of magicians in the Nahuatl world", few of which were explicitly male or female. The most well-known and broadly generic class of manipulators of the supernatural in the Aztec world were the tlatlacatecolo, the "owl-men", who were famously sent to cast spells against Cortés. These were people who specifically practiced magic against other people, but even here we have numerous subclasses of practitioners. Lopez Austin goes on to identify numerous other larger groups, including shapechangers, astrologers, and physicians who used magic, each with subclasses within them. Ortiz de Montellano (1990) specifically identifies a distinction between teyollocuani and teyolpachoani, who harm others by "eating" and "squeezing" their hearts/teyolia (part of the tripartite division of the soul).

So there really isn't a specific pointed hat, cat, and broom witch stereotype in Aztec thought. Rather, a bruj@ is one who is possessed of certain supernatural powers which they use for ill. We can see this even in Rabbit..., cites Durán extensively. He describes the most famous witch in Aztec mythology, Malinalxochitl, as "beautiful and of spirited disposition and was so clever and cunning that she became skillful in the use of magic and sorcery. Her craftiness was so great that she caused much harm among the people and made herself feared in order to be adored later as a goddess." It's not the use of magic that makes Malinalxochitl evil, it is her misuse of it in order to glorify herself and bend others to her will. The Aztecs get most press for their sacrificing of others, but they were a severe and strict people who emphasized self-sacrifice and discipline. The idea that someone would use supernatural means to advance themselves and subvert the will of others was anathema to them.

Qualifying question; Where European "Witches" actually a thing or are they a modern historical construct?

This is kind of a loaded question because "witchcraft" is a word imposed by Europeans on a range of native practices, many of which do not carry the exact same connotation. Could you perhaps elaborate on the context in which the word "witch" was used in the source? I might be able to elaborate if I know what specifically it's referring to.

Within the historical context of the Aztecs, Spanish chroniclers like Diego Duran typically used words like "witch," "sorcerer," or "magician" (edit: in Spanish typically brujo) to refer to nahualli. A nahual (or nagual, nahualli) is a kind of sorcerer that supposedly had the ability to assume the form of an animal. In many Mesoamerican religions, every human was believed to have a tonal, a kind of spirit-animal counterpart. Some powerful individuals were able to divine the identity of their tonal, which allowed them to transform into it at will. This belief is still very much alive in parts of Mexico today where it survives as a common folk tale.

The problem is, it's difficult to glean exactly how such individuals were seen by the ancient Aztecs or other Mesoamericans because of the amount of bias introduced by the Spanish chroniclers to describe them. Consider, for example, this passage from Duran's History of the Indies of New Spain where he describes how the Aztec emperor Motecuzoma I tasked a group of "sorcerers" with finding the location of Aztlan, the mythical homeland of the Aztecs:

[Motecuzoma] ordered that all the wizards and magicians who could be found in all the provinces be brought before him. Sixty sorcerers were then brought before Motecuzoma; they were old men, wise in the arts of magic. The king instructed them thus: "O elders, my fathers, I am determined to seek the land that has given birth to the Aztec people [...] Therefore, prepare to go seek this place in the best way you can and as soon as possible." [...]

Laden with rich gifts, the sixty sorcerers departed and some time later reached a hill called Coatepec in the province of Tula. There they traced magical symbols on the ground, invoked the demon, and smeared themselves with certain ointments that they used and that wizards still use nowadays - for there are still great magicians, men who are possessed, among them. One might ask, how are they not exposed? And I shall answer that it is because they conceal one another and hide from us more than any other people on earth. They have no confidence in the Spaniards and thus it is that these fiendish acts are hidden from us and kept in secret by them; and when by chance some magical practice is discovered, if it happens to come to our ears, there is always someone to cover for the sorcerer and keep him silent.

So it is that upon the hill they invoked the Evil Spirit and begged him to show them the home of their ancestors. The devil, conjured by these spells and pleas, turned some of them into birds and others into wild beasts such as ocelots, jaguars, jackals, and wildcats, and took them, together with their gifts, to the land of their forebears.

That account is pretty much par for the course in terms of historical descriptions of "sorcerers". There's clearly some historical basis for this description, as the transformation of a nahualli into his animal form is a distinctly Mesoamerican magical practice. Yet you'll notice from that passage that the Spanish priest (Duran) interjected a bit of European perceptions of witchcraft into his description. He spent a good deal talking about how they made a pact with the devil, and even included an aside reassuring his (European) audience that they were doing their best to hunt down these wizards and put an end to witchcraft in the region. Yet the fact that the emperor Motecuzoma called on them seems to indicate that the Aztecs did not quite share the same attitude regarding witchcraft.

In a very general sense, sorcery/witchcraft/magic was not something that was persecuted in Mesoamerican cultures. You could be punished for using witchcraft for nefarious purposes (for example, a healer that used magic to kill his patients warranted a death sentence in many cultures), but the act of casting a spell itself was not necessarily seen as evil. In fact, many prominent Mesoamerican kings are described as nahualli themselves. Duran, in a later passage, goes on to describe how Nezahualpilli, king of Texcoco, was described as a famous sorcerer. But on a deeper level, it's difficult to get at the exact attitudes Mesoamerican people had about "witchcraft" because the only detailed descriptions we have come from Spanish sources, which are heavily biased against it.