I am currently a very novice piano player trying to get by with Czerny's Op. 599 Practical Exercises for Beginners. As suggested, I'm playing the exercises by sight reading the notation, minimizing the amount of time I spend looking at the actual keys. I've found that the generally easiest way to do this for the mostly monophonic melodies (especially when transposing keys) is to keep track of the intervals between notes/scale degrees, forgoing any absolute identification of individual notes.
However, how am I supposed to adapt this method to full-blown chords? For example, in the following exercise, I can see that the featured chords are mostly just major and minor triads in various inversions.
I can more or less instantly put my hand in the desired shape when I see e.g. a first-inverted triad, but I don't know where to put it. When the chords are very similar in pitch or shape, I can usually manage. From bars 5 to 8 in the treble, I might read: 2nd inversion with C bass, to root position with C bass (just reshape hand), to root position with B bass (1 scale degree drop), to 2nd inversion with G bass (2 scale degree drop and reshape hand). However, this seems finnicky, artificial, and still quite hard to do in real time. It can also obscure quite obvious transformations, such as bar 1 to bar 2 being 1st degree to root position C major triads, rather than "1st inversion triad with E bass, to root position with C bass."
Experienced sightreaders, from what I hear, "just do it" without thinking. But what sort of mental activity should a beginner be undergoing when practicing this sort of thing?