You can use this converter

However it does not address bullet points (ul, li elements)

function convertHtmlToRtf(html) {
  if (!(typeof html === "string" && html)) {
      return null;
  }

  var tmpRichText, hasHyperlinks;
  var richText = html;

  // Singleton tags
  richText = richText.replace(/<(?:hr)(?:\s+[^>]*)?\s*[\/]?>/ig, "{\\pard \\brdrb \\brdrs \\brdrw10 \\brsp20 \\par}\n{\\pard\\par}\n");
  richText = richText.replace(/<(?:br)(?:\s+[^>]*)?\s*[\/]?>/ig, "{\\pard\\par}\n");

  // Empty tags
  richText = richText.replace(/<(?:p|div|section|article)(?:\s+[^>]*)?\s*[\/]>/ig, "{\\pard\\par}\n");
  richText = richText.replace(/<(?:[^>]+)\/>/g, "");

  // Hyperlinks
  richText = richText.replace(
      /<a(?:\s+[^>]*)?(?:\s+href=(["'])(?:javascript:void\(0?\);?|#|return false;?|void\(0?\);?|)\1)(?:\s+[^>]*)?>/ig,
      "{{{\n");
  tmpRichText = richText;
  richText = richText.replace(
      /<a(?:\s+[^>]*)?(?:\s+href=(["'])(.+)\1)(?:\s+[^>]*)?>/ig,
      "{\\field{\\*\\fldinst{HYPERLINK\n \"$2\"\n}}{\\fldrslt{\\ul\\cf1\n");
  hasHyperlinks = richText !== tmpRichText;
  richText = richText.replace(/<a(?:\s+[^>]*)?>/ig, "{{{\n");
  richText = richText.replace(/<\/a(?:\s+[^>]*)?>/ig, "\n}}}");

  // Start tags
  richText = richText.replace(/<(?:b|strong)(?:\s+[^>]*)?>/ig, "{\\b\n");
  richText = richText.replace(/<(?:i|em)(?:\s+[^>]*)?>/ig, "{\\i\n");
  richText = richText.replace(/<(?:u|ins)(?:\s+[^>]*)?>/ig, "{\\ul\n");
  richText = richText.replace(/<(?:strike|del)(?:\s+[^>]*)?>/ig, "{\\strike\n");
  richText = richText.replace(/<sup(?:\s+[^>]*)?>/ig, "{\\super\n");
  richText = richText.replace(/<sub(?:\s+[^>]*)?>/ig, "{\\sub\n");
  richText = richText.replace(/<(?:p|div|section|article)(?:\s+[^>]*)?>/ig, "{\\pard\n");

  // End tags
  richText = richText.replace(/<\/(?:p|div|section|article)(?:\s+[^>]*)?>/ig, "\n\\par}\n");
  richText = richText.replace(/<\/(?:b|strong|i|em|u|ins|strike|del|sup|sub)(?:\s+[^>]*)?>/ig, "\n}");

  // Strip any other remaining HTML tags [but leave their contents]
  richText = richText.replace(/<(?:[^>]+)>/g, "");

  // Prefix and suffix the rich text with the necessary syntax
  richText =
      "{\\rtf1\\ansi\n" + (hasHyperlinks ? "{\\colortbl\n;\n\\red0\\green0\\blue255;\n}\n" : "") + richText +  "\n}";

  return richText;
}

You may wish to adapt this NodeJS package: rtf2html. I understand this has already be done with an older version, as you can see in this Github repository.

After you get the corresponding HTML code, you can add it to your container using the usual DOM methods, or a library like jQuery if you are already using it.

I think the answer is that what you're looking at is typically NOT an actual <textarea>. It's a <div> or <span> made to look like a text area. A regular HTML textarea doesn't have individual formatting of the text.

"Rich-Text editors" will have controls that modify the contents of the span/div with regular html markup (<strong>, <em>, etc.) to emulate a full-blown rich text editor