At the time this question was asked, the editor was completely unusable on the four different platforms I tried. A day later, the specific issues I describe seem to have been resolved, which suggests the developer is responsive to issues. However it also suggests that this tool needs a much larger test community than it currently has. Enabling this editor so that authors on Physics would be part of the test community for prosemirror would make the experience of writing on Physics very different.
To emphasize that I can no longer reproduce these problems, I’ve hidden them behind spoiler tags.
On Safari for iOS and for desktop, the editable part of the page never loads at all. The page ends with "The text below this line is all editable, including the math! Go ahead, try it!" and a change in background color. [On desktop (14.0.3), the developer console says the definition
const REGEX_INLINE_MATH_DOLLARS_ESCAPED = /(?<!\\)\\\$(.+)(?<!\\)\\\$/; is an "invalid regular expression: invalid group specifier name." Pasting the regex from the developer console into this edit box seems to double some backslashes, and from Markdown to display seems to double some more; there are several layers of special characters here.]
On today's Firefox (87.0) for MacOS, the editable part of the page does load. Moving the cursor in and out of math-mode sections causes the display changes in the animation, and editing those things does what you might expect. However the Enter key is broken and doesn't create new lines. This makes it also impossible to write any multi-paragraph text, or (so far as I can tell) to start a new line with $$ and create displaystyle mathematics. [This behavior seems to be fixed after a comment from the author below.]
Using Firefox (87.0.0-rc.1) on Android, I get a strange behavior when I try to add text to the beginning of the editable area: I put the cursor in one place, start typing, and the cursor jumps to a different wrong place and the new text appears there instead.