Most of them are more like brief advertisements, really. Yokai Watch gets a bigger event because the franchise owner is a personal friend of XIV's director, and the Nier Automata crossover took over a big chunk of content in Shadowbringers, but most of the time they get a quick quest line and maybe a Fate or a solo duty or two, just to say, hey, here's this other game you should go buy.
The Monster Hunter crossover is the only one that really feels organic in XIV's world. Rathalos could just be another of the endless variety of dragons, the hunt bill that starts the quest blends in with the Hunt system already present, and the palico is just another talking animal. (Fun fact, if you act surprised at a talking cat while playing a Miqo'te, he immediately calls you on it. Not sure if it works for Hrothgar since they didn't exist yet.)
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