Minigames to earn Experience Points

You can already earn XP while doing almost anything on-site, you just have to be active to gain some XP and then levels: logging in, cuddling pets, sending owls and chat messages, writing and grading homeworks, creating and answering topics, completing wizard cards collections... Even sending an owl to take part in an event organised by the Plot team or the Party team of your house makes you get XP! Levels can be earned as a proof of your activity and presence on the sites you're on, and it's quite fast to obtain the required levels for grading (lvl 3), creating topics (lvl 5) and solving the Marauders' quest (lvl 10). As you mentioned, it is also possible to farm XP while cuddling pets, which is one of the easiest ways to gain levels without spending too much time or IG money, even more if there are a lot of pet owners and a list of them on your site. Thus, I don't feel the urge to ask for more ways to earn XP because there already are many. At this point, it is fair to think that any new function implemented to the sites would likely make you earn some more XP too, whether it be a new minigame or anything else.