The Gnome Shell integration add-on is listed as active. The error message is not about gnome shell integration addon, but about the “native host connector”. According to the documentation on Fedora you should install chrome-gnome-shell. This package is installed.
I installed Chromium and the website works without warning.
To clarify a misunderstanding here, chrome-gnome-shellis the browser extension (for Chrome/Chromium/Firefox/…) see link1, link2 below for more.
As for the issue, no idea. You could try a new (temporary) user account and/or a new (temporary) Firefox profile, but maybe others have better ideas on what could be wrong here. (btw, it’s working on my machine with Firefox).