Replace your code with this

         <div key={`${"asdf"}-${idx}`}>
          <input
            type="text"
            placeholder="Enter text"
            value={field || ""}
            onChange={(e) => handleChange(idx, e)}
          />
          <button type="button" onClick={() => handleRemove(idx)}>
            X
          </button>
        </div>

i have used a third party debounce , you can choose anything you want

code

import React, { useState } from "react";
import AwesomeDebouncePromise from "awesome-debounce-promise";
import ReactDOM from "react-dom";

import "./styles.css";

function App() {
  const [fields, setFields] = useState([""]);

  function handleChange(i, event) {
    const values = [...fields];
    values[i] = event.target.value;
    setFields(values);
  }

  function handleAdd() {
    const values = [...fields];
    values.push("");
    setFields(values);
  }

 function handleRemove(i) {
   const values = [...fields];
   values.splice(i, 1);
   setFields(values);
 }

 const searchAPIDebounced = AwesomeDebouncePromise((event) => {
   console.log(fields);
 }, 100);

const submitHandler = async (event) => {
  event.preventDefault();
  const result = await searchAPIDebounced(event);
};

return (
  <div className="App">
    <h1>Hello CodeSandbox</h1>
    <form onSubmit={submitHandler}>
      <button type="button" onClick={() => handleAdd()}>
        Add Input
      </button>

      {fields.map((field, idx) => {
        return (
          <div key={`${idx}`}>
            <input
              type="text"
              placeholder="Enter text"
              value={field || ""}
              onChange={(e) => handleChange(idx, e)}
            />
            <button type="button" onClick={() => handleRemove(idx)}>
             X
            </button>
          </div>
         );
       })}
      <button className="margin-top" type="submit">
        Submit
      </button>
    </form>
   </div>
  );
 }

export default App;