Magic, a key plot point in the PA series, is a powerful force that has been used to perform feats such as summoning a magic barrier around Hachiko High School, resurrection and the summoning of powerful deities. Characters have often been subjected to its effects in different ways, e.g. death (fitting given the story’s general themes). However, its general rules are largely undefined within the series, often a consequence of using it within other forms of fantasy media.
Magic Users[]
Given the obscurity of Catscratch as a language, due to the dominance of dogs and as a result Doglish being the most spoken language, the majority of the magic users in the series are cats such as Coco Grimalkin and Mittens Wichien (a full list of magic users can be seen here). However, there are a few exceptions to this rule who happen to be dogs: Ginger Claret, due to having a shared common magic user ancestor with Whiskers and Mittens (divergent evolution is wacky that way), and Patches, as he made the effort to study Catscratch with the help of Felix for the purpose of summoning Bapawmet (technically, he was in the body of Angel at the time, and he had only studied it for that specific goal. One possible interpretation is that even back in his original body he could possibly study it further).
In terms of cats who don’t study magic or don't have potential for it, Tigger is far more focused on athletic prowess and another exception is Angel, due to being the adopted brother of Coco (whenever Angel has magic potential is unknown: possibly not, however). Ironically, given his status as the Elite Magic Club's vice president, it has been inferred that Whiskers lacks any magic ability, although he still studies it regardless (however, there is also ambiguity surrounding this. Given that recent post game info given by Denny has been stated to not be taken as gospel, audiences are free to interpret this however they want).
The only place where magic has been stated to be practiced is within Kemono Woods Private School, via the The Elite Magic Club. However, given that the canon ending has the cats and dogs of the series being on better terms with each other, it’s unknown what happens to it after the current ending of the PA series.
Magic Wands[]
Magic usually requires a wand as a conduit for spells. Wands are usually powerful and rare artifacts, often family heirlooms. Most magic users cannot use magic without a wand, but some extraordinary magic users may simply use their paws, for example Ginger. As a design choice, magic wands are typically some sort of object, reflecting the personality/interests of its user, affixed to a stick. For example, Coco's is a star, reflecting her classic nighttime witch persona while Mitt's is a ribbon, reflecting their vain yet prim demeanor.