I'm really sorry to hear about this. The .ru (Rambler) hack is quite common where hackers immediately change the primary alias, which is why Microsoft says your email 'doesn't exist.'
Since you are seeing the hacker's email on your desktop apps, you should try the Account recovery immediately, but use the new email (the hacker's one) as the account you're trying to recover, while providing your original details (old passwords, previous billing info) to prove ownership.
Also, for those who are trying to calculate the potential loss or impact on their digital assets/data during such hacks.
Steps you should take right now:
- Use the Microsoft Interactive Tool for hacked accounts.
If you had a credit card linked, contact your bank to freeze it immediately.
Check your browser's saved passwords; sometimes the 'old' alias is still cached there and can help in the recovery form.
Hope you get your account back soon!