Out of all of the storage apps (and you NEED to go in knowing that this is a companion app and not a full on game), My Pokemon Ranch quite honestly was the most quaint/fun one. This app has a built in regional Pokedex checker that allows you to see if you are missing Pokemon in Sinnoh, and you can catch it. The Pokemon all have interesting actions that they can take just by watching them. Some will use their moves that they know, others may be shy- these are all determined by their natures. You can get additional interactions through daily objects. Back in its prime, you could even visit other peoples' ranches via the WiiConnect24 feature, which as of writing has been offline for exactly a decade.
Unfortunately this game does not have compatibility with Platinum which is a shame because Diamond and Pearl are super slow. Japan got Platinum compatibility alongside some exclusive event Pokemon.