how to avoid brownout caused by a multimeter on esp32
To prevent this problem you select a small value resistor to put in place of where you are at present trying to place the multimeter for the current measurement. Then use the meter in voltage mode to measure the voltage drop across the resistor. Using Ohm's law you can compute current from voltage divided by resistance.

The meter internally uses this same technique in the current mode. However at whatever current range you were using the meter's internal resistance is high enough that the net voltage drop is sending the MCU into the brown landing zone.

Another technique that can be used is to power the unit from an adjustable bench power supply where you can tweak up the source voltage slightly to compensate some for the drop for a series multimeter in current mode. Care must be taken with this though to avoid running your target device at a voltage above its ratings.