Alright real quick, lightning speed:
http://megamitensei.wikia.com/wiki/List_of_Persona_3_Items ctrl+f lightning As for the attack lightning being cloud to ground, well, it comes from a cloud and it hits the ground (The dodge animation is wonky so I wouldn't use it anyway, but it's a thing)
https://youtu.be/JaOw71pcK60?t=33 (Look at the last one, you see a bit of cloud, also it moves vertically and all that, IIRC, easier to see with zionga and stuff)
As for the anime being less contradictory, lolno.
Due to it's nature as an adaptation literally every time it decides to change something it's a contradiction with the source material, for example:
-Yu getting his persona earlier than he is supposed to
-the entire thing of Kanji losing his glasses mid fight
-Yu destroying Naoto's dungeon
-The entire margaret fight
-Shadow Mitsuo and Izanami pulling that weird illusion stuff The list goes on.
As for the so called contradictions of the arena games:
Himiko literally changed into a combat form, of course it's gonna have new abilities, why would someone include that.
Movesets in general being different is an obvious concession needed to make them fit into a fightning game roster, also it's been months, them trying out new moves isn't exactly out there to begin with, regarding the ultimate personas:
"From the P4A art book: Why do all of the "Persona 4" characters' Personas appear in their initial form? Wada: "Persona 4" differed from "Persona 3" in that the evolution of your Personas depended on your Social Links, so that aspect of the gameplay experience would have been different for every player. At the very least, we knew that every "Persona 4" player would have seen all of the Personas' initial forms during their playthrough, and that's why we decided to use those forms in "Persona 4 Arena."
Why a sequel with the same studio involved in the story department being non-canon is even being debated is beyond me. But in persona 5, P4D is refferenced with Kanamin, Arena is refferenced in a tv thing. etc... PQ being canon or not doesn't matter since everyone was buffed during the events of that game anyway but it's worth noting that it went out of it's way to erase all traces of it's existance so as not to contradict the timeline. Also if you feel like including animu feats despite all this then by all means, But discounting Arena whilst counting it is a massive double standard.