First you seem to be confusing the charger modules with the buck converters. They use completely different chips.
Mine looks a bit like the one in your picture.
No confusion, you might be right that i may have been sold a defective unit but i dit not confuse annything.
Were are speaking about boost / step up regulators, something that takes <5V in and will output 5V.
I ordered two of those of ebay sold as "5V DC boost Converter", i am not the brightest bulb in the chandelier but i can assure you i can measure a simple dc voltage.
Both of them had the same sawtooth output, maybe they are not 5V regulators but something different but they are sold as boost converters and i tested them under various loads.
The threadstarter has a input voltage from 2 to 3V and wants a 3.3V output.
You suggested modifying the feedback network of one of these chinese 5V boost regulators to achive 3.3V output.
Nothing wrong with that, but...
You do not know what you buy, you have no datasheet of these devices, you do not know what idle current they have, no idea about the efficiency, you do not know annything about them.
Shure you can buy one of each wich are currently available, test them, evaluate them and maybe out of 10 modules one has the specs you need.
Then you set out to buy a crate of them and the seller no longer has them in stock, there may be another one on alibaba wich looks the same but you do not know if it is.
We are speking about a battery powered device with runs in a MCU controlled power down mode that draws <50µA. Something wich needs to run extendet periods of time on a battery.
The best regulators from name brand companys have idle currents (quiescent current) lower then that and a efficiency above 50% in that load range.
Why should a random boost converter you pluck of ebay, alibaba, ali express or what not meet those narrow parameters?
And... one other thing, if you build something you may want everything on one neat PCB, neat and tidy, low profile, known dimensions. No chance dooing that with the china regulators.