I find slow practice is how I learn to play the right notes. If I make more than one mistake in a "practice" of a piece, then I slow down.
It takes 3 to 5 perfect sessions on a piece at any given speed before the learning moves from the cortex into the inner motor circuits. I mean perfect, NO mistakes. After that I can speed up a little. Usually 10% or less.
My teacher taught me this starting 1958 and it has served me well. Even when I go back to pieces I learned 50 years ago, a few stumbles to figure out what fingering I was using, then the inner brain kicks in and I have the piece down nearly perfectly again. I should have written down more fingering numbers, the ones in the book never worked for my ethnically different hands.
I mean it. Practicing while making mistakes just sinks them into the brain, just like the correct movements should have. Going too fast too soon, means IMHO, no progress at all. I don't know how students in conservatories do it, the breakneck pace, but I've never wanted to be a professional. If you do, you had better have more innate talent than I do. I play things correctly, but it takes a while, usually starting one hand alone for weeks and weeks.
Teachers won't tell you this IMHO because they don't want to discourage you, and want their money. Stumbling around making mistakes keeps you going back. Since I restarted piano and organ about 2000, I've had three lessons. One was about emotion and interpretations, not the correct notes. The other two, one was about organ bench posture, and another about the names of the sounds of the pipe organ.
As far as scales, I did those early plus Schmitt, then Edna Mae Berman exercises, follows by Czerny School of Velocity. I did exercises about 10-15 minutes every practice session back when. this IMHO will give you mastery of nearly all the physical tricks required to play the piano. If you have a teacher to point out the secret lesson of each exercise. Grinding though the exercises without a guide IMHO is useless. the physical tricks are not explained on the printed page.
Hoping for faster progress for you.