Lower sales than last year doesn't really indicate saturation considering 2020 and 2021 were two of the best years of any platform. NS is more so in the mature phase of its run if anything as its sales are still quite considerable. 

Pokemon Arceus has successfully launched a new branch of the franchise The Pokemon Company must be worth an insane fortune. 

Doesn't sit right with me thinking a Switch 2 debuting next year when you put out a jaggernaut like BotW 2 the year prior. If the game gets delayed, yeah, I can see it, too.

Has anyone the Famitsu first week sales of Pokémon Sword/Shield and Diamond/Pearl (Switch) to compare it with Arceus?

Pokemon First Week Physical Sales:

Pokemon Black / White: 2,637,285
Pokemon X / Y: 2,096,050
Pokemon Sun / Moon: 1,905,107
Pokemon Black 2 / White 2: 1,618,621
Pokemon Diamond / Pearl: 1,586,360
Pokemon Omega Ruby / Alpha Sapphire: 1,534,593
Pokemon Gold / Silver: 1,425,768
Pokemon Legends Arceus: 1,424,657
Pokemon Heart Gold / Soul Silver: 1,408,980
Pokemon Brilliant Diamond / Shining Pearl: 1,395,642
Pokemon Sword / Shield: 1,364,544
Pokemon Ultra Sun / Ultra Moon: 1,199,814
Pokemon Platinum: 967,675
Pokemon Fire Red / Leaf Green: 955,337
Pokemon Yellow: 851,091
Pokemon Crystal: 707,580
Pokemon Let's Go Pikachu! / Eevee: 664,198
Pokemon Emerald: 643,987

Idk the stock situation in Japan. But Nintendo mentioned they expect switch to break the trend of declining sales for Nintendo hardware, so they are probably going for that #1 spot. Regardless, I do expect it to follow DS trends.

Well Nintendo just declared there were shortage issues with the OLED model.

And it's sold out on Amazon Japan for reference.

So basically the same as gold and silver…. Not counting digital. I wonder what are the total sales, and if it is able to match sun and moon, since digital is much bigger now, than in the 3DS era

A new Pokemon that finally changes up the formula after 20 years and a brand new model to refresh the market and still a decline. This is really worrying, especially since it might not be a long slow bleed out.

I'm not surprised by the hardware boost being much lower compared to the last major Pokemon releases but just under 100k almost 5 years in is still strong and Arceus is doing amazing.

Think of it this way, the Switch should do around 20m this year so the decline in 2023 and onwards would have to be massive to stop around there. The successor would have to release in Spring next year to make that possible basically.

So if next year the Switch does 10 million, 50% drop, is that a cliff?  I could see 20 million this year, 10 next and 5 after.  Puts it around (ballpark) 135 million total.