I believe I can add some valuable insight to this discussion. My qualifications are 45 years working in the NVH field. The first 40 years for the world’s largest manufacturer of small engines and the last 5 years for the largest manufacturer of motorcycles in the USA.
First, regarding the kite video it is apparent that a component in the kite is causing an impact noise possibly to the camera case itself. This is the sharp rapping or knocking sound heard. Second, GoPro cameras are notorious for wind noise. With the open back case, wind only a few miles per hour will be very audible.
Professional wind screens are made of special open-cell foam about 4 inches in diameter and are designed to minimize any effects on the frequency spectrum. We routinely used them in our indoor facility to protect the expensive microphones ($700) from damage should the stand inadvertently be knocked over. For the typical wind speeds encountered a few hundred feet above the ground they would do a good job minimizing wind noise.
I found a paper from Montana State University called “Summary of Gun Shot Acoustics” which has a lot of good information about recording the sound of shock waves for rifle bullets. The link is here:
https://www.montana.edu/rmaher/publications/maher_aac_0406.pdf
For velocities just over Mach 1 the angle of the shock wave is nearly 90 degrees to the travel of the rocket. This would make it impossible to hear from the ground as has been stated before.
I think the biggest problem will be distinguishing the sound of the sonic boom from the sound of the rocket motor. If the noise level of the motor is 10 dB or more above the sonic boom it will be very hard to separate it out. The noise from the rocket motor is broad-band noise caused by turbulence of the rocket exhaust “tearing” at the (comparatively) still surrounding atmosphere. The sonic boom is a short impulse called a “N” wave due to its shape. Possibly it could be “dug out” of the rocket jet noise with careful analysis.
I think recording a sonic boom from a model rocket is going to be extremely challenging. Kudos to the first person to accomplish this feat.
Tom