My current teacher is a graduate of a conservatory in Lithuania, she is in her 60's so that would have been part of the USSR at the time she was there. I can only guess that she was a disciple of the "Russian school".
I'll call myself a reasonably competent amateur, with no goal other than improving. I sought out a teacher after I realized after a re-dedication to the piano that I was only going to get so far relying on lessons taken almost 40 years ago supplemented with YouTube videos. I did not seek out a "Russian school" teacher, she was available and had impressive credentials so I signed up.
Whether or not this is because she is from the Russian school, or just a good teacher, I do not know - but it's technique, technique, and more technique. So much technique. I never remember a teacher devoting this kind of time to technique. Hand positioning, lifting the fingers, how the wrists rotate in arpeggios, relaxation in the hand, focusing on which muscles are engaged etc... And while I've developed some bad habits over the years, many of them are being addressed and it's making a difference in my play.