Have your tried emailing their customer support? I know you have tried to use chat and the website to contact support but I think a direct email would be simplest. They are quite used to getting messages in English (and actually request this on their website). This is the address to use: support@yoomoney.ru
Another reason I suggest this is because there is a discussion here where one guy says "Send the help desk an email. It was fixed for me in 1 hour."
https://www.reddit.com/r/AskARussian/comments/1n3cmkb/is_it_possible_to_create_a_yoomoney_account_from/
Based on information online (summarized by Google AI), there is a common problem where many foreign phone numbers are automatically blocked, but customer support can manually unblock the number for you.
Personally, I did not encounter any problem receiving codes from YooMoney via SMS to my international phone number, but I have found that I am unable to receive emails into my Outlook email from many Russian senders. Though, curiously, this does not include YooMoney, whose various emails reach me fine.
So if you email support but don't get any reply, it may be that your email is blocking messages from Russia. One way to get round that is to set up a Russian email account. This can be done for free through mail.ru, where you can select English as the set-up language.