Yes, that's another law they have. Can't access the internet anonymously, basically. And yes, foreign phone numbers do work.

Though I've seen, plenty of times, smaller places have a "public" wifi with a password, and the password is just written on a piece of paper somewhere. That must technically violate that law. But you know, laws in Russia...

The first and last time I was in Russia was in 2019, passing by Moscow airport, and you already required a phone number to use the public WiFi, but any foreign number was OK.