I have seen similar (but just similar) questions here, so I decided to ask anyway.
What is a buck-boost module, preferrably from Aliexpress, that I can use to power an ESP32 with 3.3 V from a 3.7 V lithium battery, with a 500 mA budget?
Despite an LDO like the AMS1117-3.3 going all the way to 1 A, it wouldn't make the cut because the lithium batteries can go down to 3.2 V.
I found a module with the HX4002B charge pump chip, but it goes just up to 150 mA.
You don't need a buck-boost. You need a buck that switches to pass mode when the input voltage is too low.
The ESP32 doesn't need exactly 3.3V. It needs at most 3.6 V (maximum allowed, do not exceed) but works properly down to about 2.5V.
All you really need is a buck converter that drops the voltage to 3.3V.
I've used some LM3671 modules for this very purpose. I've had a couple of ESP32 modules running from solar charged battery banks for several years now. They work just fine with the LM3671 modules regulating the voltage from the lithium cell.
