In the process I accidentally connected GND of the BME280 to 3V3 on the NodeMCU and VIN to GND. I realized when the temperature sensor did not work at all in the beginning (but this was also caused by the firmware to be configured to use the DHT22 temperature sensor).
After correcting the connection and the settings, the SDS011 is working fine, but the BME280 delivers values that are a totally off. Temperature -146.9 °C, pressure 616.67 hPa, humidity 100%. Also these values stay constant over time.
Hmm, the problem occurs both with the charger which I got from nettigo (Output 5V, 1500 mA) and a USB power pack I am running the whole setup from now which, according to the writing on it, delivers up to 5V, 3.1 A.
Regarding the solder points, please see the pic below: