Hi Vladimir,
I am really sorry for the delay of this reply as it is a weekend for us here.
I can reproduce your issues, but I noticed when I copy this URL http://xn----7sbbbxobldi6b5anbe7c2j.xn--p1ai/vhod/registratsiya in Firefox browser address bar, then it redirect to http://публикация-статей.рф/vhod/registratsiya , so it show this error
ERROR: Invalid domain for site key
http://xn----7sbbbxobldi6b5anbe7c2j.xn--p1ai/vhod/registratsiya (Google chrome)
http://публикация-статей.рф/vhod/registratsiya (Firefox)
Can you check with your webhosting provider regarding this? why it auto changed the site URL?
Second thing is, can you capture a screenshot what site URL you register from your Google account?
https://www.google.com/recaptcha/admin
** If you wouldn't like your site URL display on public forum, I will remove it, because I would like to explain to you what my investigated result.
Hope you understand.
Looking forward of your response.