The Export Note component in Shortcuts work well (using the excellent scripts posted by roar), however it appears at the moment to lack an option to select base64 Images as well as the other options available in the Bear UI.
Not sure if it is possible, but even just enabling the option for base64 images when exporting to HTML would be quite handy.
In the meantime, export to PDF is a reasonable substitute, although not quite as smooth when images break across pages.