[old_tv_nut]

"Say, I have a pattern, that is, a complex frequency. If I want to make it brighter, I increase the carrier frequency, but then my whole pattern moves to the right, so a frequency that was, say 2 MHz, becomes 2.5 MHz, which means it is a different pattern!"

Exactly right. It is a different frequency spectrum.
This should not bother your understanding, as in the luma input time domain the high frequency ripple pattern is riding on an average background level; in the frequency domain, the luma baseband input consists of the high frequency plus some DC (zero frequency) energy representing the average background brightness.

After FM modulation, in the frequency domain, the sideband frequency, determined by the high frequency pattern frequency, is "riding on" an average carrier frequency determined by the average brightness of the background. In other words, if the average brightness is different, the average carrier frequency is different, and all the associated sidebands move to keep their same frequency distance from the average.

You should also understand that the diagrams show the frequency bands that are available to carry the FM signal, not the actual FM spectrum that is being sent in the available band in a particular case. The flat top of the FM range just indicates that the FM carrier and sidebands will be recorded if they fit in that range. If the sidenbands go too low in frequency, they will be cut off and their pattern will not appear in the output image. That's what happens in the extreme example where a very high frequency luma pattern is riding on a dark background. In this case, the average carrier frequency is lower, the sideband shifts lower by the same amount as the average, and it gets cutoff by the low end of the system response curve.