Why is the independence war going on, when I'm no longer his vassal anyway?

Solution 1:

First of all, make sure that you've let the game run for a month or so to see if the war ends, it runs checks against the validity of the casus belli of the war at a regular schedule, not as that condition becomes true. If you still keep fighting, the issue is probably related to the equal-to-liege revolt "title" you get when you declare independence - your highest title was already ducal when the Basilius granted you a de jure duchy, so perhaps the game doesn't realize that you have actually gained a de jure ducal title. You could try switching the de jure ducal title to your primary if you haven't already and see if that fixes it. If none of this does, you may just need to finish the war and hope that you win, because I have no clue what would happen to your title if you lost (you could make a save, try it and report back).