i randomly remembered pokemon ranger and playing it a lot as a kid: en.wikipedia.org/wiki/Pokémon_Ranger

i have a lot of nostalgia for this one and it doesn't seem to be talked about much; it had unique gameplay where you used the stylus to make circles and shapes that would surround/"weaken" pokemon into being captured. if the pokemon managed to break the lines you drew too much, the "device" your character used would break, but i remember getting a "game over" wasn't too punishing. reminds me a lot of pokemon go in a lot of ways, feels almost like a predecessor, but i never see it discussed anywhere

would definitely play well on a mobile emulator too