Admittedly it does appear that there is a lot more evidence that I initially thought but I still have some thoughts. These quotes seem to be talking more about how the games are canon in relation to each other rather than encompassing all Pokemon media, especially the Pokemon Adventures manga. They state that different games can represent what is possible within Pokemon, but that seems to be referring to Pokemon as a franchiese. If I remember correctly, Hidenori Kusaka, the author of the manga, is not affiliated with GameFreak in any way, so scaling the Adventures manga to the anime and games still seems highly questionable.
I don't see it as such, he may not be with Gamefreak but it's clear that the company has great influence on the manga with their rules about canon writing and what is and isn't allowed in the game. With a developer saying the manga is what they envision the world would look like, I'd say it's very much confirmation that this works properly.
Why wouldn't this be evidence that the two continuities have different mechanics and are thus separate?
Because they don't beyond minor differences that usually can be attributed to moves having various effects, something that happens within the media itself as well.
There are lots of other contradictions as well, like the anime blatantly ignoring core mechanics of the games like type immunity
No they don't, that's blatantly wrong. Either the immunities are bypassed via outside methods like using water to bypass water immunity with a pseudo-Soak, or they are very blatant errors that don't get repeated again. There are errors in the anime, they are very much errors that don't get repeated again and shouldn't be considered.
In addition, the events of the anime are never brought up in the games.
They're parallel universes, I never said they're in the same universe. Ash and Alain do exist in the games too though as evidenced by Ash-Greninja and ash cap Pikachu existing and Steven mentioning Alain in Oras.
It still seems clear to me that the anime and games, even if sharing a cosmology, function on different laws.
They do not, at all, the evidence you brought up is based on errors in the episodes that never get repeated. Bring up something else as evidence.
Even if Pokedex entries are the same across these different mediums, I do not believe that is sufficient evidence to conclude that the Pokemon in each medium share scaling
It's scientific research in-verse that is consistent across all timelines. I don't see how that's not conclusive.
especially when they display feats of varying impressiveness different from each other.
They do not, otherwise, prove it.
As a notable example, Pokemon in the games have difficulty dodging most moves while in the anime they consistently dodge moves that should have 100% accuracy.
This is ignoring official animations specifically made to represent ingame events like Origins and Twilight Wings (or even that one Bidoof animation) which clearly show Pokemon dodging attacks with ease, even 100% accuracy ones. The pokedex outright talks about mons dodging attacks too.
Them not dodging much is very clearly a game mechanic that is very common in RPGs.
