To declining sales in Japan ?
As things stand yes, they will remain a major actor but with dwindling influence, they seem to be ok with that and made peace with it, not everyone has though apparently
Highlighted part isn't really true. There have been some Momotaro Dentetsu games on PlayStation (and even one on Xbox 360, TIL), but with nine releases on PlayStation versus 17 releases on Nintendo, I think it's fair to say it's mainly associated with Nintendo.
The nuance might be worth mentioning yes, but from 1997 to 2006 the IP was indeed closely associated with Sony, it had a few main exclusives (7, V, X USA, XV), the best selling titles by far (7 at 770k, X V and XI at ~500k, you can check
here) that there were a couple handhelds only titles that sold a meager amount and a couple multiplatform entries whose sales were for the largest part on Sony platforms, doesn't change that.
The years after the PS2 was when the IP popularity waned and Konami stopped releasing games, the Wii entry then had a spectacular resurgence after it was feature on TV in the mid 2010's, it prompted Nintendo's effort to contact Konami for a series revival on 3DS and the rest is what we're witnessing right now.