<p>text1 <br> text2 </p>

.red-text {
  color: red;
  background-color: #FFEFEF;
}

const wrapAfter = (el) => {
  const { childNodes } = el;
  const src = childNodes[2]; // 0: text, 1: <br>, 2: text
  
  const wrap = document.createElement('span');
  wrap.classList.add('red-text');
  wrap.appendChild(src.cloneNode());
  el.replaceChild(wrap, src);
};

wrapAfter(document.querySelector('p'));