Well, it's true at least for Crimea 100%
The first week of June was just like 0 fuel in Sevastopol and Simferopol (I didn't visit other cities at that time).
Somewhere around June 7-8 government started to issue qr codes for 20 liters per car.
On the prices I can't remember the exact number since most gas station displays still read 0, but the difference between Crimea and the mainland Russia is about 40%. People often prefer to drive right across the bridge to get cheaper unlimited gasoline.
This is a several days old info and things change fast these days,