How are your modules connected to the LDO? If there's long wires or traces in the path, the inductance there may be an issue. Connecting something like an 10uF decoupling cap between gnd and 3v3 may solve that issue. It was the bloody wires and or the breadboard I use to prototype this. I soldered ...

Hi! I have a bunch of different esp32 bare modules that I jut can manage to power with voltage regulators due to voltage drop causing brownouts. Unfortunately I have no way of measuring such low currents ATM, only a DMM. I first tried a bunch of low iq LDOs from aliexpress: MPC1700, HT7833 and HT733...