Used the official Raspi4 power supply. Should be enough: after unplugging it delivers power for about 15s.... and Raspi won't boot up during that time. Very nasty in view of missing reset button.
The WiFi problem looks like a bug. If I start with low resolution, the 2.4GHz network works nicely. If I go to 1920x1080 wlan0 either shows "not available" or so, or it shortly shows a neighboring network labeled with a red "5G", depending on what I click at the top of the screen, but my 2.4GHz network is not recognized. With my router set to 5GHz (+2.4) it works.
So, if there were a power problem, it must be within the Pi4B board (Copper traces too thin?).