The BME680 requires i2c write to configure and trigger the measurements, and i2c read to get the data afterwards. If you are getting data that makes sense (e.g. increase in temperature when touching it, decrease in gas resistance when bringing alcohol close to the part, etc.) Then everything works as expected. Seeing that your current consumption measurement seems static, my best guess at this stage would be to say that your current measurement setup is the issue here. The BME680 draws on average ~1mA(avg) when used in LP mode, and ~100uA(avg) when used in LP mode. However, the current consumption while sensing gas is in excess of 10mA ! You need a current measurement setup that can sample at a high rate and make the average over time. o_o
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