Animisha In one of the September practice challenge videos, she shows herself in a practice session where she starts with a phrase, does just the intonation, then adds the dynamics. So I think just practicing the notes with the tempo is ok, then adding other layers one at a time. As long as you don't do too many repetitions before you have all the layers in place, it's ok to build up this way. And she says if you can't get the notes quickly, make the section even shorter until you can, and start building from there.
I get impatient and try to do everything at once on sections that are too long, instead of breaking it down to as small a piece as I need to in order to set myself up for success. Honestly, I have an unhelpful belief that makes me rush: I started in my 50's, so I'm "behind" and need to "catch up" "before I die without achieving my goals." I think that's why I rush.
But I'm eating the elephant too fast and choking on it, so I'm not saving myself time by rushing!
Piano is so humbling.