The outerHTML method of the LiteAdaptor incorrectly does HTML character escaping on elements whose contents are PCDATA, such as <style> and <script>.
This can be fixed in
https://github.com/mathjax/mathjax-v3/blob/d60e0ec1650ffcfeeee9ff216c386cb87cadb50a/mathjax3-ts/adaptors/lite/Parser.ts#L341-L348
but checking of the node.kind is in the constructor's PCDATA object.