I now officially know how to improvise. I just did it enough over a few tunes so that the harmonies became second nature. Then I learned "Autumn Leaves" in twenty-four hours and I can improvise to that. So I could theoretically do that with any song that I learned. Whether I can improvise well is another question, but what I mean is that I don't play wrong or unintended notes and don't get lost in the form, and that I can even camouflage mistakes when I do make them.
I can figure out a walking bass line for a chord progression.
I still play too basically in terms of left hand technique and putting extra voicing notes in the right hand. I am still at the level below mediocrity but I can play things that sound ok to people who don't know jazz very well or are not over critical. On Easter I played at a family gathering for a while and people thought it was good.
I have noticed that I sell myself short in a lot of respects. I have a desire not to seem arrogant. But this desire also causes me to not excel in certain areas or to take full ownership of everything I do, even in my scholarship. It's very odd. I imagine that many people also sell themselves short in many ways, perhaps not even realizing it.