Well. I was wrong that the signal generator offset is calibrated during autocalibration. No, it is not calibrated. Only channel offsets are calibrated. I "fixed" my oscilloscope.
Thanks to @pcprogrammer. His post #185 clarified a lot, including the ADC type (MTX2088). After checking the datasheet, I tracked down where the reference voltage for the ADC is formed. What a quest, I tell you. Due to the aggregation of essentially 8 ADCs in 3 possible configurations, the reference voltage to the ADCs comes through analog switches from two sources. But I found it anyway. I reduced it from 1.237 V to the required 1.18 V by fiddling with the voltage divider. After that, the oscilloscope began to normally show signal amplitudes without an error of -7%. The offsets floated away a lot. After autocalibration, the offsets returned to normal. This did not affect the signal generator offset in any way, apparently it is calibrated at the factory. However, the accuracy of the signal generator offset did not bother me, unlike the oscilloscope.
It is still necessary to thoroughly investigate whether my modification has damaged any functions, but at first glance everything is fine. This problem could easily be solved in the firmware by adding a manual calibration mode using a reference signal, but here you can only rely on Fnirsi.
But my joy was overshadowed by the fact that I found another bug, much worse than the predictable systematic error, there is no time for perfectionism here... When trying to measure a signal with a frequency of 85 kHz and an amplitude of 40 Vpp, I encountered the fact that the touchscreen began to glitch indecently, and sometimes the interface even completely froze (measurements continued). Then I went further and tried to measure the voltage of 160 V and a frequency of 46 kHz, and then just dancing began. Multiple false touches. And it is enough to connect only the ground clamp to start the problems. Here you have battery power, here you have galvanic isolation from the AC-line. This is a failure. I have come to the conclusion: capacitive touch control and oscilloscopes should live in different worlds.