This might be a bit of an odd and in many ways contrarian take imo, but I'll say it anyway.
But in my opinion, and I say this after having played through several Pokémon games back to back over the past few months, I feel that the Pokémon games can really be divided into four different "eras" of Pokémon imo in terms of what makes the games' identities and what they are. But I feel they can be divided into something like this:
Original era: Gen 1 and Gen 2
Second era: Gen 3 and Gen 4
Third era: Gen 5 and Gen 6
Fourth era: Gen 7 and Gen 8
These aren't super rigid categories imo, but I feel there is enough convergence between each gen I listed together to combine them into a single era. Each "era" I made constitutes a set of games that are alike from each other, but have distinct differences from the rest and have their own identity together. In a sense, each "era" here constitutes not only a different generation of kids who got into the franchise, but I feel each era forges a different identity and interpretation of what a Pokémon game "is".
Each generation I converged together has enough similarities together and combined are different from each other era that you can feel tangible changes with each era of games and what people who enjoy the Pokémon games value about them. Gens 1 and 2 are obviously alike, being the basic beginning of the Pokémon games and what makes them well, Pokémon to the kids who grew up with that is distinct from what other kids from later generations value about a Pokémon game. Even today, they are still very much distinct from every future generation of Pokémon that came afterward.
Gen 3 and Gen 4 are very much alike as well: while there are some tangible differences between the Hoenn games and Sinnoh games, they are also very similar in more ways than one, same with FRLG and HGSS in that regard, and the things people value about the Hoenn and Sinnoh era are very distinct from what would be valued about other games. The Hoenn games reinvented the wheel for Pokémon with many new changes, and the Sinnoh games rode on that even if they made some changes themselves too. Many of the similarities between RSE and DPP include the region structure, the way the plot is structured, and the features and content you get: Contests, Secret Bases, Battle Frontier in Emerald/Platinum, and all that. Many of the routes between the two regions are also similar. This was also the beginning of cover legends being relevant to the story, in which the base games has one of each summoned and awakened, and then both are brought together in the 3rd version with the "third legendary" intervening.
I also feel similarly about Gen 5 and Gen 6: some people claim that Gen 6 tried to reverse the blowback and made itself very different from Gen 5, but I disagree: on the contrary, I think the Unova and Kalos games are much more alike than they are different. For one thing, Gen 5 did really make a lot of reinventions and changes as to what Pokémon is, which is a big part of why it got a lot of blowback at the time imo, but Gen 6 I feel really took after the things that Gen 5 changed and followed suit as well, even if it also brought some changes with it. But in many ways, the Unova and Kalos games share many things in common: much like Hoenn and Sinnoh, Unova and Kalos are pretty alike as well, both having notably more linear structures than regions of the past. Unlike the past four regions which were based in regions of Japan, Unova opted to be based on a western region, being based in New York, and likewise, Kalos opted to be based on France. The protagonists of Unova and Kalos are also older than those of the past, with Hilbert/Hilda, Nate/Rosa, and Calem/Serena all being implied to be in their mid teens. This is unique to these regions, as the Alola and Galar protagonists are on the younger end. There was a much stronger focus on story in these games, with BW, BW2, XY, and even ORAS all being based on having a story to tell and having more human, fleshed out NPCs. There are no singular third versions this time around with either generation. The cover legendaries are also story-involved again, and this time you are required to catch them (not in ORAS, but in Unova and Kalos most certainly yes). The way BW1 and XY take off their stories is also similar in that you start off with a group of friends "chosen" by the professor of the region, and one is a more formal rival (Cheren and Calem/Serena) while the other is just a friend who follows you through the journey (Bianca and Shauna/Tierno/Trevor). There are also many other similarities Unova, Kalos, and ORAS had between each other in that regard that they can be conglomerated into a singular "era" of iterations of what defines a Pokémon game.
The most recent, and current era, imo starts with Sun and Moon and continues into the present day. I feel Gens 7 and 8 also are similar to each other in a sense and together form a distinct new "era" of what makes a Pokémon game. The Alola and Galar games really share similarities as well: chief among these is a bigger focus on the League, with you officially being acknowledged as a Champion at the end of the adventure. Alola and Galar play with the traditional League structure, as the former did away with Gyms and did the "Island Challenge" consisting of Totem Pokémon and Kahunas, while Galar returns to the Gym Leaders but does away with the Elite Four, instead replacing it with a tournament where you go off against fellow people competing to claim the Champion title. The "villainous team" of these games is less serious, with Skull and Yell both not being that severe of threats, with the actual antagonist of the game being someone you wouldn't expect (Lusamine and Rose, respectively). There is an even stronger emphasis on making dynamic and human characters in SM, USUM, and SwSh, more than ever, which is a big defining trait of the Alola and Galar games I feel. While there are some differences between them, they also have a lot of similarities to converge them into one big "era" of Pokémon. I am not sure how BDSP and Legends will take after the Alola and Galar games, but that doesn't take away from the similarities in the identities of defines SM, USUM, and SwSh. Opinions on this era are pretty divisive right now, but as it stands the kids who grew up with this particular era of Pokémon are still very young and are not yet old enough to be in online communities, which lopsides the perception of this era quite a bit imo.
And overall, you may notice a trend with these. Each odd numbered gen is the experimental testing ground, the generation that reinvents the wheel with what a Pokémon game is, with Gen 1 obviously being the debut of the series as a whole, but Gens 3, 5, and 7 all reinvented the wheel in their own ways and the even numbered gen that followed effectively stayed true to its preceding odd numbered gen, often ending up more popular than said preceding gen due to debuting on a new platform and bringing in a new wave of kids.
This is probably a very contrarian take and one not many probably thought about, but this is a conclusion and opinion I came to after really looking back at many Pokémon games in hindsight imo.
