Adding to the superstition question.. are "poke religion" or even any kind of superstition a thing here? Is there a specific region or group that has different rituals to different beings?
I'm going to say 1.) depends on the region, and 2.) depends on what you consider a religion. While many real-life religions are centered around a deity/pantheon, it's not a strict requirement, as the only definite feature of religion is the devotion to a specific ideology. When talking about theistic mythologies in particular, it's worth noting that many of them have stories dedicated to explaining the natural world. Humans hold a strange combination of rationality and imagination, after all, and we like to apply meaning to entropy. But in the Pokemon universe, many natural occurrences already have an explanation: the legendary pokemon. From forces as undeniable as the weather to as intangible as life/death itself, it's widely recognized that legendaries are the driving forces of the globe. It begs the question, in a world full of creatures that are powerful beyond imagination, what even is considered a god?
In my au, the thing that sets legendary pokemon apart from other pokemon (including mythicals) is belief. Unbeknownst to the general population, belief in a legendary pokemon's power is what gives them their power in the first place, and should that belief waver, so would the pokemon's abilities. For example, Groudon and Kyogre are cemented in the Hoenn mythos as almighty forces of nature that quite literally shaped the entire continent. With their abilities to control the very land and sea, they could potentially wreck the globe---and nearly have multiple times---simply because humanity believes they can. The only thing that's stopping them is everyone's faith in an even higher power: Rayquaza, whose job is to protect the planet and keep balance from its domain in the sky. Their limits, or lack thereof, exist on a spiritual level rather than a physical one.
Additionally, these beings seem to be functionally immortal, or at least are long-lived enough to survive thousands of years and mold the Pokemon world into how we know it today. Based on in-game information, most of them don't need to reproduce, either---it's as if they simply spawned into existence. Their origins and lifespans are simply incomparable to any other pokemon.
That does sound pretty god-like, right?
At the same time, they're just like any other pokemon in a way. In real-world mythologies, gods usually have a vested interest in their domains in some way, and the ones that don't tend to be less personified manifestations of natural occurrences (take Gaia, who, besides Being The Earth and creating the Titans, isn't very active in the Greek mythos). Meanwhile, legendary pokemon are often ambivalent to the rest of the world at best. It's not necessarily that they consider everything beneath them, but rather that they hardly take notice of it any more than most people would take notice of an ant under their shoe. Might ants think of humans as divine because of their might and incomprehensible ways, in that case? Or are legendary pokemon truly just creatures that happen to have capabilities no living being should possess?
Let's return to the actual question that was asked: what about religion itself?
The most widespread religion in my au, though by no means the only one, is best described as Arceus-centric creationism... but that's a bit of a mouthful. I'll be referring to it as Arceism from here on out. Practitioners are Arceists, and anything pertaining to the religion is called Arceist as well. Of course, there are more religions that are more region-specific and self-contained, but we won't be diving into those very deep.
First off, I don't think it's realistic for every single region to have the exact same religion. From a Doylist perspective, we know for certain that Arceus is the creator of the Pokemon world. However, throughout the games themselves, Arceus is hardly ever significant or even mentioned, so I think it's safe to assume that in it's more of a background figure in everyday life. Also, there's the fact that isolated peoples will naturally develop different cultures, and by extension, different religions. A massive reason why certain real-world religions have become such powerhouses is because of colonialism, and... yeahhhhhh no thank you. The way I imagine it, Arceism spread with the Ancient Sinnohans' diaspora, and wherever it landed, it either fizzled out or managed to integrate itself with the preexisting local traditions to varying degrees of success.
As for the actual culture of Arceism...
As briefly mentioned, Arceism originates with the Ancient Sinnohans, but modern Arceism would be much different compared to its earliest practices. Assuming the timelines between the Pokemon world and the real world are comparable, and that PLA does take place around the late Edo/early Meiji era (think the Meiji Restoration), that's around 150 years of cultural shift. The Ancient Sinnohans were already long gone by the time PLA takes place, so you could easily add at least a century to place the start of Arceism. Additionally, my inspirations for the two periods are quite different---my ideas for the Ancient Sinnohans are somewhat derived from the Saami, but I also think it would be interesting for modern Arceism to mirror Islamic practices due to the gothic mosque-like exterior of Hearthome's Foreign Building (the Pertevniyal Valide Sultan Mosque is a good conparison imo). There will likely be elements of Shinto as well---despite my earlier prattling, I personally consider the true nature of legendary/mythical pokemon to be closer to kami than the gods of western ideologies---but the degree will vary depending on the region. All this being said, while I'm not going for 1:1 representation, using real cultures as groundwork means that I would like to get a little more research under my belt before I decide anything concrete regarding Arceist practices, values, etc. Plus going into specifics might possibly double the length of this post........
For now, let's zoom in and examine the unique cultures of some different regions!
Kanto, as the setting of the very first Pokemon games and therefore lacking some of the series' classic formula, doesn't place too much emphasis on its legendary pokemon. It makes sense, in a way: Kanto seems to be a place of modernity and progress, especially when we see how it changes in the three short years between the Kanto and Johto games, so it doesn't have much time to dwell on parables of the past. Besides a general acknowledgement of Arceism, religion is relegated to smaller practices scattered across the subcontinent--take the channelers for example, who are clearly inspired by Shinto priestesses and only appear in Lavender Town (gyms don't count). Meanwhile, superstitions mostly spread as urban legends, The sighting of unusual elemental bird pokemon is a common one that has been recorded for centuries, but the most infamous tale revolves around a dangerous creature that lurks in a cave outside of Cerulean City. There are no concrete facts about its origin or appearance... only that the very few who have encountered it barely escaped with their lives. Was it luck that allowed them to see another day, or a conscious act of mercy? Such distinctions continue to be the subject of forum debates to this day.
With community being such an important pillar of Johtonian life, it's no wonder that Ho-Oh, the overseer of the Brass Tower and therefore of the connection between people and pokemon, has become a venerated figure in turn. Not only is its silhouette a national symbol, the Brass Tower is also one of the most popular tourist spots in the region. But in addition to reverence, legends of its power inspire fear as well. As such, Ho-Oh's name is one that is invoked aloud only in the most desperate prayers and solemn promises... much unlike Lugia's, who is hardly spoken of at all. The guardian of the seas has been all but lost to time as people's memories burned along with the Tin Tower. However, there is one group of people who haven't forgotten this sacred beast: the Dragon Clan. To them, Lugia stands at the top as the fiercest dragon of all, and so much of their cultural worship revolves around it. The whirlpools that occasionally appear in the Dragon's Den without cause are even said to be signs sent from Lugia itself, warning of troubled times ahead.
In Hoenn, the super-ancient pokemon are regarded as the penultimate beings. After all, although Arceus may have brought everything to creation, it is the very earth, sea, and skies that impact our everyday lives. After being separated by Rayquaza the first time, Kyogre and Groudon are said to have escaped their dens to battle again on two separate occasions: the spring and autumn equinoxes. Therefore, those are the most common times for people to leave offerings at the many dedicated shrines located around the region. It's also considered bad luck to make too much noise for fear of waking the legendary pokemon, so most people will stay home and keep to themselves. Conversely, the day following each equinox is dedicated to celebrating Kyogre/Groudon's inactivity as well as Rayquaza's continued protection. The largest of these festivities take place at sunrise at the Sky Pillar and is headed by the Draconid people, beginning with a ceremony inside the Pillar itself. No one knows what the ceremony actually consists of, since very few people are even allowed inside, but the reemergance of the Draconoids signals an official end to the silence---this event is televised so that eveyone across the region can see.
Unlike many other regions, Sinnoh's Arceism is closer to a soft polytheism---that is to say, Sinnohans view Palkia, Dialga, and Giratina (whose influences have been largely confined to their origin in Sinnoh) as different archetypes representing aspects of Arceus's domain. However, Ancient Sinnohans saw these legendary pokemon as strictly separate beings, and many modern Ancients (the term for practicing descendants of Ancient Sinnohans) carry on with hard polytheism. It's theorized that the truce between the Hisuian Diamond and Pearl clans inspired this shift in ideology, but a lack of definitive proof makes it hard to confirm. Despite this, the Hisuian era of Sinnoh's history was an undeniably formative time, with many traditions, occasions, and beliefs carrying into contemporary culture. For example, it's a still common stereotype that West Sinnohans tend to be punctual and impatient, while East Sinnohans are detail-orientated to a fault. A pairing of the two will be either picture-perfect or an utter disaster... or so the saying goes. It's really no more accurate than the compatibility between astrologic zodiac signs, but there are some people who swear by the notion nonetheless.