This is a question I have toyed with as far back as Art College. My own conclusion was the same. Jesus does not qualify as a zombie.

For one thing, he was resurrected, not merely reanimated. He wasn’t “walking dead”, continuing to rot. He “came back to life” as a fully restored human, with intelligence and memory. He didn’t crave brains for sustenance.

That said, tho, his tale does include many of the tropes of vampire lore, including rising on the third day and compelling his followers (even now) to drink his blood.

(In the name of full honesty, it should be noted that vampires borrow much from the mythology of Jesus, not the other way around.)