Not sure he classifies as not famous but if there was an award for the greatest combination of classical and non classical piano playing on the planet and even perhaps of all time I think it would go to this pianist who goes by the name Cateen. I am going to post his YouTube channel because it's really impossible to choose just as few of his amazing videos although I included just a few.
https://www.youtube.com/@cateen_hayatosumino/videos
He is a good enough classical pianist to reach the semi finals of the Chopin competition, one of the very most important classical competitions on the planet, and you can see some of his performances from that competition on his YouTube page. Cateen will be giving his Carnegie Hall debut in the upcoming year and has a recording contract with a very exclusive label.
As far as his non classical playing goes(here I'm referring to non classical but also non jazz style), the only pianist I know who can match him is Peter Bence who doesn't perform classical although I'm sure he had classical training since he has a sensational technique.
As impossible as it sounds, Cateen did not attend a conservatory but did get a master's degree in engineering.