Is there a relationship between transonic buffet magnitude and altitude?
Transonic buffet, or Mach induced buffet, or high speed buffet, is a flow separation due to the combined presence of shockwave and "high" angle of attack. The boundary layer separation results in random high frequency vibrations. As the AOA increases, the separation and the associated vibrations worsen, up to the point where the crew can no longer read the instrumentation and perform normal flight duties; this point is called deterrent buffet.

For a single Mach number, the AOA (or $C_{L}$) associated with buffet onset is generally constant; there will be some differences due to CG position, the associated trim and Reynolds number effects. During aircraft design and flight testing, the buffet onset boundary similar to the one below is mapped out. As you can see, the general trend is a decrease in buffet onset boundary with Mach (though the trend can reverse depending on the airplane).



(Image modified from https://www.researchgate.net/figure/Typical-buffet-onset-curve-and-separation-mechanisms-defining-the-boundaries_fig2_270086469.)

Flying at the same Mach number at a higher altitude means that it will have smaller dynamic pressure than flying at a lower altitude. This translates to a higher AOA at the higher altitude, which means that the buffet intensity will be higher. In other words, for the same Mach and weight, the maneuver margin is decreased the higher it flies, independent of its climb capability.