Zod Schema: How to make a field optional OR have a minimum string contraint?

In your case, you consider "" to be the same as undefined (i.e.: when the string is empty, it’s like there’s no string at all).

It’s implementable in Zod this way:

import { z } from "zod";
import { strict as assert } from "node:assert";

// `myString` is a string that can be either optional (undefined or missing),
// empty, or min 4
const myString = z
  .union([z.string().length(0), z.string().min(4)])
  .optional()
  .transform(e => e === "" ? undefined : e);

const schema = z.object({ test: myString });

assert( schema.parse({}).test === undefined ); // missing string
assert( schema.parse({ test: undefined }).test === undefined ); // string is undefined
assert( schema.parse({ test: "" }).test === undefined ); // string is empty
assert( schema.parse({ test: "1234" }).test === "1234" ); // string is min 4

// these successfully fail
assert( schema.safeParse({ test: "123" }).success !== true );
assert( schema.safeParse({ test: 3.14 }).success !== true );