BKN1964 Perhaps a little background would frame your expectations... help us offer pertinent suggestions, rather than assuming you know more, or less, than you do.
Since you've had formal training, and are returning to the piano, you must already have some idea about scales and chords. But you haven't said where you're at, other than wanting to learn jazz.
Do you plan to play in a group? Or are you just going solo? Are you hoping to play "Standards", cocktail type jazz piano, or what? What "jazz tune" or tunes do you play now? What song or songs would you like to play?
Personally, I find the chord/scale relationships endlessly fascinating. You can separate the two, and either learn scales and proper fingerings, or chords and their inversions, or work on them together. Either approach will bear fruit, and after a while, (different amounts of time for different players), you will internalize what you have learned.
To improvise requires knowing what you can play within the song structure, essentially which notes of what scales will sound good, or at least make sense, with the chords. To do this, on the fly, you need to have those chord/scale relationships in your bag of tricks. And the other thing you need is the ears to be able to "hear" the changes and how what you're going to play will sound.
If you plan on reading the sheet music to songs and improvising based on the written chord changes, you can learn what scales to play over those chords, thereby learning some scales in context. Then pick another song and do the same. All of Jamie Aebersold's play-a-long books offer a scale syllabus for the solos, showing which scales work with the changes. His #54 "Maiden Voyage" has a nice selection of tunes played at comfortable tempos. You can also turn off the piano side to play along with just bass and drums, once you feel comfortable enough.
https://www.jazzbooks.com/jazz/product/V54DS
At any rate, keep at it, ask questions of other players, maybe try to find a teacher, and above all, listen to the jazz players who play the tunes you'd like to play.