Otter

Holds things, drops them, picks them back up. It would hold your hand if the pixels allowed for it.

Adopting one takes a tap and no account. It grows through five stages over about sixty days, it cannot get sick and it cannot die, and it is never sad at you for being away.

The wallpaper is 1080 by 2340, which fits nearly every phone made since 2019. The card is an animated GIF, so it works anywhere a picture does.