Kirby crossovers with adventure themes often lean into the portal or dimension-hopping premise, which is a classic setup. You get Kirby popping into another world, and the humor comes from his simple, food-motivated perspective clashing with more serious settings. I've seen a bunch where he lands in something like 'The Legend of Zelda' and just inhales a Guardian, leaving Link baffled. The trope of Kirby's 'friendliness is a superpower' gets played up a lot—his innocent demeanor disarms grimdark characters, forcing them to lighten up.
Another recurring thing is power scaling debates made narrative. Writers love to test Kirby against other powerful characters, not just in fights but in how his copy abilities morph when he eats, say, a Heart Container or a Chaos Emerald. It becomes a weirdly creative exercise in system fusion. Also, the 'team-up with local hero against a greater threat' is almost a given. Dedede and Meta Knight might get dragged along too, causing their own brand of chaotic diplomacy. The adventure usually stays pretty light, even in darker crossover worlds, because Kirby's essence is so stubbornly cheerful.
I think the tropes work because they preserve the core contrast. The fun isn't in making Kirby edgy, it's in letting him be a pink wrecking ball of positivity through someone else's complicated plot.