i slightly think I have to disagree @Tatoruzu the turtles do have spirituality . Leonardo Raphael Donatello and Michaelangelo splinter would most likely pray to human dieties in the Shito buddah spirituality ninja came from cryptids prophets and arcahic gods and devils the sidhartha, the tengu, onriyo, oni, raijn, fujin, yokai like kappa, gardura, nagaloka, sun wukong etc. something about pre mutated splinter has a mystical supernatural aspect about him plus combined with the ooze is what made splinter live so long than an ordinary rat and he mimics human behavior such as martial arts pre mutation and post mutaion he has a photographic memory, cause real rats have a short life span you can teach em tricks like playing basketball balls or running through a maze etc. splinter lived well passed his expiration date in the life cycle of rodents. andrew modeen and arsiney dubakov non canon fan graphic novel conclusions to the mirage verse tmnt origin and tmnt odyssey tmnt 2023 brought to the turtles such an interesting over looked aspect as splinter is a sorcerer supreme like dr. Strange in asian mysticism in most incarnations such as mirage 2003 show next mutation and rise. in guest artist michael zuli take on the turtles as more like a Akira kurasowa take on tmnt as samurai esque in souls winter splinter and the turtles worships a primitive demon called "Animist" and beseeches him to save the life of one of the turtle deciples who was gravely injured and dying from having one of their sword arms cut off by one of the foot ninja in the battle of central park against shredder, I think Splinter is not an ordinary rat but a foot mystically endoued animal with hamato yoshi warrior essence. like how splinter was possessed by the turtles forgotten ally Gosei hattori elder in the passing, or the time when the foot in image tmnt wanted to posses splinters body after he was cured from his feral bat personality secondary mutation, or in vol.4 tales where he had a battle on the astral plane with a foot mystic he turned into a vegetable, or choosen to be the god of rats replacing the rat king in the pantheon in tales of the tmnt, he also exercises orroku nagi haunting tang shens old home when they visited chihaya Akasaka village where he came from, also i like the aspect of archie adventures series changing the rats name to ogata the name splinter would have to be a nickname from the turtles i dont see him being called that by yoshi so the archie adventures series named the rat that touched splinter "Ogata" which is a Japanese sounding name for hamato yoshis pet rat sounds fitting than him being named an americanized name, but I never liked the take of the 87 toon trying to make sense of splinter origin making him a human and then idw or platinum dune michael bays reboot cheaply copying this aspect and making the turtles and splinter all reincarnations of ancient samurai warriors because the Hollywood trope of some how ninjas can't exist in the modern day it robs tmnt of its authenticity and charm and makes it even more ridiculous trying to explain and ground an anthropromorphsized trend of talking animal character parody of Dave simm cerebus frank miller ronin Daredevil and jack kibry kamandi grounded in realism.
Technically I think the turtles are pseudo Shintoist pseudo Taoist and pseudo Buddhist in a way because kinda like for example the nation of islam is to sunni and shite Muslims their Christians incorporating moorish science temple information jim jones evangelist and scientologist ideology and nothing really sunni or shite Muslims malcolm x muhammad ali or khallid muhammad went to mecca to study, But in the case of the tmnt they follow the religious cult of bushido because also you have to remember splinter learned all he knows from a secret clan of ninja spec ops and assassin cult that allows domestic abuse on women in the honor code of the samurai copying the weeb frank Millerisms of the wolverine lone wolf and cub and ronin.