Mahayana or Theravada, or any other offshoot. Is a Buddha an exception? Or a personification?
It is not personification. There is evidence that Gotama Buddha exists in India. He is special so he was called Samma Sambuddha.
when the Buddha is designated a sammā Sambuddha, "a perfectly enlightened one," this highlights not only the fullness of his enlightenment but his authority and reliability as a spiritual teacher.
Why does good householder Ilya, so long and often wisely involved, as such a fullish question, actually knowing for her self? Why would on join a "Tathagata-form" at first place, if perceiving him as common?
Everybody, seeing the Dhamma could see the Tathagata, and in as far every not blind person could reach same "Tathagata-hood", once there, is common under Arahats. And also "fox and sour graps"-thinking is common under those not inside or heading toward different ancestorship.
Although householders question could be marked as special unwise, it's actually common under common. If liking common... well then... the world stands open for such.
[Note that this isn't given for stacks, exchange, other world-binding trades, nor for delight in pseudoliberalism, but for escape from this wheel]