It looks like your PCB does not have a I2C level-translator (3.3-5V), instead only using 4k7 resistors. Most BME280 boards have IC/MOSFETS for this.
So -ve currents will flow when 5V TX happens feeding into 3.3V part with 4k7.
The sensor has many modes and you can change the sample rate, filtering to lower current drain.
I found the Adafruit BME280 Arduino library gave high temperature readings. Several degrees C higher than should be read
It might have a bug reading the calibration table for temperature. Tried another library and it was better. Bosch's C code is heavy on floating point for an Arduino.
Let me know how your temperature readings are.
The BME280 is sensitive to light, no bright light while reading it.