JSFiddle - React, Tailwind, and code Playground

HTML

<form id="form" action="">
    <textarea name="" id="txt" cols="30" rows="10"></textarea>
    <br />
    <input id="btn" type="button" value="Вывести текст" />
</form>
<div id="txt_block"></div>

JavaScript

document.querySelector('#btn').onclick = function() {
    var text = document.querySelector('#txt').value;
    text = text.replace(/\n/g, '<br>');
    document.querySelector('#txt_block').innerHTML = text;
}