BKN1964 Would it be best to focus on one scale/key at a time and learn it inside and out, or get proficient playing the scales first with correct fingering, then memorizing the notes, then learning the chords of that scale, then learning the extensions?
Jazz Piano already requires so much rote practice that I find applying drills to actual tunes very motivating. Even though the actual practice is still very rote, by the end of practice you find that you have improved your ability to solo over that particular tune.
Autumn leaves is a good one to start with, since it can be as easy as one or two scales that are applied to the entire tune. Practice this "solo" drill: pick which scales you want to use over which chords of the tune. Then you will solo over the tune's chords using this method: use a left-hand voicing you feel very comfortable with. (The left-hand can be as simple as playing half-note roots.) In the right hand, start on a random in-scale note and ascend the scale using eighth notes (but keep track of where you are in terms of the chord progression of the solo, and play the left-hand accordingly). When you reach the highest in-scale note of the piano, descend without stopping, going as low as is practical before going up again. If you reach a chord that requires a different scale, switch to the new scale as smoothly as possible (i.e., pick the closest higher/lower note in the new scale), without stopping your eighth-note rhythm. You may not be able to use standard fingerings when you transition between scales, but try to get back to standard fingering as soon as it's convenient. You can modify this drill by randomly or systematically choosing a highest/lowest note to play, changing key, using triplets, changing the left-hand voicing, using arpeggios instead of scales, picking up the speed, etc.
I don't think you need to learn a tune in all 12-keys, particularly at the beginner level. If you simply switch tunes every few weeks, and you make a conscious effort to try to choose tunes that are in a variety of keys, you'll pick up the most important ones reasonably well. At some point, you might start learning a few of your favorite tunes in at least one or two more keys, as it helps you think of notes as their relative intervals instead of their absolute pitches.
Scale/arpeggio practice doesn't give you much in terms of creativity. If all you do is scales/arpeggios, your soloing will sound robotic (possibly a fast robot if you've been practicing well!). The big advantage is that it will give you more ability to execute your creative ideas. If your scales are internalized, then any in-scale melody you create in your head becomes far less challenging to reproduce with your fingers. I always do this kind of practice when I first start learning a tune, to give me a foundation from which to build.