How to explain and possibly avoid undervoltage on I2C bus?
@Ale..chenski is right: After freshly compensating the probes, the undervoltage was gone.
I had compensated the probes with the attenuation set to 1x, at which setting they were still perfect, but had recently switched to 10x, not knowing that this requires recalibration.
The I²C communication problem could be fixed by turning on clock stretching, as described in the updated question.
Thanks everybody.