Make the lentil-walnut ragu: Select the Saute setting on the Instant Pot and let the pot heat up for a few minutes before adding the oil. Once the oil is hot, add the onion. Cook until the onion is beginning to brown, 4 to 5 minutes. Add the garlic and cook for 1 minute, tossing frequently to prevent burning.
Add the za'atar, cumin, oregano, paprika, and cayenne and stir frequently for 30 seconds until the onion is well coated in the spiced. Select the Cancel setting.
Pour in the vegetable broth to deglaze the pan, using a wooden spoon to scrape up any browned bits on the bottom of the pot. Add the lentils, walnuts, salt, and black pepper to taste. Pour the diced tomatoes on top, but do not stir, allowing the tomatoes to sit on top (this prevents the tomatoes from blacoking the Instant Pot's heat sensor and burning).
Secure the lid and set the Pressure Release to Sealing. Select the Pressure Cook setting at high pressure and set the cook time to 16 minutes.
Meanwhile, make the tzatziki: Use a box grater to finely grate the unpeeled cucumber. Place the grated cucumber in a fine-mesh sieve or wrap it in a clean, thin kitchen towel (or several paper towels) and squeeze out the excess water. Place the nondairy yogurt in a medium bowl and add the grated cucumber, garlic, dill, salt, lemon juice, olive oil, and black pepper to taste. Stir to combine. Taste for seasonings, adding more salt as needed, more lemon for acidity, or more dill for fresh herb flavor.
Once the 16-minute timer has completed and beeps, allow a natural pressure release for 10 minutes, and then switch the Pressure Release knob from Sealing to Venting to release any remaining steam.
Open the pot and stir well. To serve, spoon the ragu onto the wraps or pita and top with shredded cabbage, diced tomatoes and cucumber, and the tzatziki.