I would give you a count if I could. My guess is on the order of thousands, but not tens of thousands. Seems like the browsers are trying to download every single note I've ever created at once (from looking at the network requests and seeing the huge amounts of data being transferred).
Also, just tried loading the site on a much faster internet connection and everything worked, although text entry was slightly laggy on a new note. Still couldn't figure out how to get a count of my notes though.