If you don't own a food processor, mash chickpeas with a fork and shred hearts of palm with two forks pulling apart so the vegan tuna retains a chunkier texture.
If you want controlled creaminess, stir mustard, lemon juice, and ½ cup cashew mayo into the chickpea mix, then after noodles cool, fold in remaining ½ cup cashew mayo for coating.
For a well-chilled salad, chill the assembled pasta for about an hour in the fridge so flavors meld before serving.
If fresh peas aren't available, cook ½ cup frozen peas according to package directions, cool fully, then stir into the mix for crisp bite.
When making ahead, store salad in the fridge up to 5 days in an airtight container to maintain freshness.