In sleep mode, the BME680 consumes <1µA. In forced mode, the BME680 triggers the measurement of only one sample of temperature/pressure/humidity/gas (as configured by the user), then goes back to sleep mode. During the actual sensor measurements, the current consumption would be quite higher than you mentioned (see datasheet for full details). We also don't know if your measurement is an averaged current, or what is your BME680 configuration/data-rate.
Since you are measuring the total board current, we would recommend to measure the current consumption of each components, otherwise we couldn't conclude that the current is drawn by the BME680. You also pointed out that you are using I2C, which could lead to leakage current in your system. After power-up sequence, the BME680 automatically starts in sleep mode, this could be a useful reference before checking that the BME680 isn't going back to sleep.
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