You could put TeX code in a script tag <script type="application/x-tex"> ...TeX code... </script> and process it using a javascript TeX-to-DOM process

You could put TeX code in a script tag <script type="application/x-tex"> ...TeX code... </script> and process it using a javascript TeX-to-DOM processor... seems likely somebody, somewhere, has done that? Update: I just read the rest of the comments and discovered KaTeX.