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Fire/Fairy could have biblical angel inspiration, they were fine using Jewish mythology.
Psychic/Bug could maybe be a Vespiquen counterpart or rival, leading its colony not through a hivemind but a network with psychic powers (maybe Durant related too?). Aren't there also parasites that capture a host and control or influence its mind? Parasect uses a fungus parasite but we haven't had an insect parasite yet, like a flatworm.
Poison/Ice we could have a Greenland shark, which resides in the coldest possible waters and has toxic flesh.
Normal/Ghost we could have a tanky Hachiko ghost reference, maybe with a special defense version of Stamina, or maybe it stays in battle a turn after its HP hits 0 like a reverse Mimikyu? Would be a cool reference to his loyalty.