What is the expected current for BG700A-GL during network search? I measured 86-100 mA at 3.3V, probably depending on the band searched. It seems very high to me.
Once the module was connected (LTE Cat M1 DRX = 1.28 s) the current dropped to 10.5 mA, which is better than 16.5 mA specified in the datasheet. This suggests that the measurement setup should be OK.