So I was a (mostly Funk/Jazz) bass player for a long time, and as a bass player, I had a strong understanding of music theory. The reason that I had such a strong practical/intuitive understanding of music theory on the bass was because intervals between notes on the bass is always clear when playing a song. For example, a perfect fourth from any note is always one string over on the same fret, no matter what note you are playing. This made it really easy and fun to improvise chord progressions because you don't have to change your fingering to play the same chord type or the same scale type on the bass.
Then I started to learn piano, and I found it really frustrating because, although I know the theory, improvisation is extremely difficult for me still because "seeing" the intervals and the scale patterns/chord patterns on a keyboard is much harder than "seeing" them on a fretboard.
I have been practicing "seeing" the pattern for a chord/scale for a few months now, and although I have gotten better at it, I still find that I am way too slow to do live improv of chord progressions (which I could do on the Bass) because of the nonuniform nature of the piano. It is difficult to keep track of quick scale changes and to immediately identify the pattern for a chord/interval jump in the same way I would be able to on the bass, because the fingering is different for every root note. Seeing chords and inversions is equally as hard as a result.
So my question is this: do pianists actually memorize the note names of every single chord/scale (e.g. memorize Db Major7 Add13 is Db F Ab Bb C) and think about that while improvising/playing live? Or are pianists able to "see" the chords and intervals by quickly being able to "see the pattern" like you would be able to on the bass? If its the latter, then what are some things I can do to get faster at "seeing the patterns" of chords and scales?