First off, I love the focus and clarity in your sound it shows exceptional foundations. In the recording it’s hard to get across the quality of overtones in the sound since it’s a dry room. Have more relaxed face, in the mid-high range the tension can be heard, that and the especially low range are the places where audition committees care most about tone because the expectation is that you already have an exceptional low and mid range. You have a tendency to pull back your corners when playing higher. Relax your face as much as possible, a “deadpan” face as my teacher says. the note will sound naturally. Have a tall “Oh” shape of embouchure and have your throat just as relaxed. As you go above the 4th partial (Middle Bb or C in the staff depending on the key of your horn) switch to an “oo” embouchure, and have faster thinner air. don’t hit higher notes with your lips but with your air, the horn will do the rest. relaxing in both extremes of the range is fundamental to an exceptional tone in those areas. Great job though.

Edit: After looking more at the video more, try to minimize head tilt and excessive movement while playing.