I meanwhile ended up using the buster-backports kernel 5.4.0-0.bpo.3-amd64. It seems the only way to avoid the nasty bug having to switch VT to get the monitor back on after blanking/power save. The Intel X11-driver has other drawbacks.
While dealing with that problem quite often (also when upgrading 2 Lenovo-Tx20 laptops) I observed following with Ivy-Bridge and Sandy-Bridge CPU's): This problem manly happens when I first boot into another OS and thereafter into Buster without power cycle. Happens i.e. when you upgrade Stretch using a VT and finally reboot. Also happens when I save the complete Buster partition for backup using i.e. Clonezilla or on my PC where I have dual-boot with Stretch and Buster. This problem seems to dissappear with time when further exclusively booting Buster. Could it be that in Buster the GPU is not reset/initialized correctly and there are some settings remaining from previous boot/configuration?