Whisk the eggs with the milk and salt until no streaks of white remain. Set aside.
Set the Instant Pot to Sauté on Normal. When the display reads Hot, add 1 tablespoon butter and the onion. Cook for 3 minutes, stirring, until soft and translucent.
Add the venison in a thin layer. Let it sit for 2 minutes without stirring, until the underside browns, then break it up and cook for 4 to 5 minutes more, until no pink remains and a thermometer reads 71°C (160°F). Add the garlic, ginger, paprika, and pepper and stir for 30 seconds, until fragrant.
Add the soy sauce and stir, scraping the bottom of the pot to lift any browned bits. Transfer the meat mixture to a bowl and leave about 1 teaspoon of fat in the pot.
Add the bok choy stalks and cook for 3 minutes, stirring, until bright and just tender. Add the leaves and cook for 1 minute, until wilted. Drain any liquid by tilting the pot and spooning it out.
Switch the pot to Sauté Less (or cancel the heat). Add the remaining butter, return the venison, and pour in the eggs.
Stir gently with a spatula, pulling the eggs from the edges to the center, for 2 to 3 minutes, until they form soft curds, look glossy but not wet, and no raw liquid remains. Turn off the pot and let it sit for 30 seconds.
Spoon into bowls, top with scallions and chili crisp, and serve immediately.