Well, Highlight API ( https://developer.mozilla.org/en-US/docs/Web/API/Highlight ) should just work inside <textarea> too.

At least it works in my Sciter like this:

    <style>
      textarea::mark(myHighlight) {
        background-color: yellow;
        color: red;
      }
    </style>
    <body>
       <textarea>Lorem ipsum dolor sit amet</textarea>
    </body>
    <script>

      // Select a range of text to highlight
      const range = document.createRange();
      const textNode = document.querySelector('textarea').firstChild; 

      range.setStart(textNode, 6); // Start at the 6th character
      range.setEnd(textNode, 11); // End at the 11th character

      // Highlight the range
      range.highlight("myHighlight")

    </script>

Ask your browser vendor to enable highlight API in <textarea> too :) so such tricks will not be required.