Can Google Process Cyrillic URLs & The .рф TLD?

Short answer: Yes, Google can.
In May 2020, John Mueller clarified that:

IDN TLDs should be fine, they’ve been around for a number of years now.

IDN stands for Internationalized Domain Name, and there are a number of variants including .рф, .قطر (Qatar), and .ایران (Iran).

What is a .рф domain?

In Cyrillic, .рф translates to .rf, and is used for Russian Federation websites. As of February 2016, there were more than 900,000 registered.
Examples of this domain in live use include:
  • онлайнбилет.рф
  • волонтёрыпобеды.рф
  • ярче.рф
  • красстрой.рф
  • сушиселл.рф
  • дешеваяаптека.рф
  • серебрица.рф