In the past, with incredible obstacles to swift communication, isolation led not only to local practices becoming the rule in a certain place as well as practices becoming more and more differentiated between different places. A bit like island ecology and evolution, where isolation produces bizarre plants and animals (think Australia and marsupials).
So up to 50 years ago, you could differentiate between a German school of piano playing, a French school of piano playing, an English school of piano playing and a Russian school of piano playing. They emphasised different approaches to piano technique and different areas of strength in the repertory. (more about that in a moment). Why only these four schools? Why not a Japanese school? Mostly because there was no tradition of piano playing in Japan, and Japanese pianists to be ended up studying with a teacher that paid allegiance to one of the four schools.
However, in the past 20 years (and even before that) as communication bloomed, and as information became widely available, such distinctions pretty much ceased to exist with pianists over the world synthesising all the information and arriving at personal ways of playing that take the best from each school.
As far as I am concerned there is no such a thing as a “national school” of piano playing, and mostly people will use this sort of labelling as a marketing device. “Have lessons with Bernhardovsky, a legitimate representative of the Russian School”.
Have a look here where there was some discussion on this subject:
https://www.pianoforum.net/cgi-bin/yabb/YaBB.cgi?board=perf;action=display;num=1070796095https://www.pianoforum.net/cgi-bin/yabb/YaBB.cgi?board=teac;action=display;num=1080170595Now for the national stereotypes:
Leschetizky (1830 – 1915) claimed he could tell the nationality of a player by just listening to him/her. Here are his conclusions:
English – Good musicians, good workers, bad executants.
Americans – the most spontaneous of the lot.
Russians – The best. Prodigious technique, passion, dramatic power, elemental force and extraordinary vitality.
Polish – Leans more to the poetical side of the music. Originality, refinement, exquisite tenderness, instinctive tenderness.
French – Birds of passage, fly high in the clouds impervious to what lies below. Dainty, crisp and clear-cut in their playing, they phrase supremely well.
Germans – Command respect for their earnestness, patient devotion to detail, orderliness and intense and humble love of their art. But they can be a bit grey.
Swedes – Gentle, talented and sympathetic.
Italians – Italians “love” because they are Italians. But as a rule they cannot play the piano in the very least.

Best wishes,
Bernhard.