The 10th Anniversary Supplement was out for a while, but I somehow forgot to check it out until today. So...
The first thing that strikes when seeing the new Azumanga is how much Yotsuba influenced its style, especially around faces and in the beginning. But the effect lessens along the way and the manga returns to its roots. It really is amazing, because it's as if Azuma-sensei rediscovers himself in front of your very eyes. Even the storytelling for each strip gets stronger towards the end.
Lord of the Universe
The supplement creates new canon, there can be no two opinions about it. Extensions were extremely mild so far, although we may be certain they broke some fanfics somewhere in the long tail. But I wonder if Azuma-sensei ever considered making drastic changes, just to prank fans? Sadly, he stopped short of giving Kagura a given name.
The Solomon's Solution
That said, the Creator of Azumanga is somewhat amenable to tackling issues that fans were asking about; explaining, if not changing anything. Perhaps answering the same question in every interview on the topic was getting old.
And Most Importantly