What I'd do is update your div to use an onKeyDown like this:

const socket = new WebSocket("ws://localhost:5000");

const Chat = () => {
  let divText = "";

  const sendMessage = (event) => {
    alert("submit");
    event.preventDefault();
    console.log(divText);
    divText = "";
  };

  const handleChange = (e) => {
    divText = e.target.textContent;
    if (e.key === "Enter") {
      sendMessage(e);
    }
  };

  return (
    <div className="chat-div">
      <div className="chat-box">
        <span className="razmak"></span>
      </div>
      <form className="input-form" onSubmit={sendMessage} spellCheck="false">
        <div
          className="chat-input"
          contentEditable="true"
          onKeyDown={(e) => handleChange(e)}
        ></div>
        <button className="send-button" type="submit">
          jhgj
        </button>
      </form>
    </div>
  );
};

export default Chat;

There's a couple of other things, some which I've not included above:

• Lowercase the method names if they don't return JSX
• The divText should ideally use the useState React hook
• Consider using a standard input rather than a div, as this is semantically more correct, and accessible for people using screen readers.