I am planning to try out STM32 blue pill and black pill to replace my Arduino Nano. I learnt here that Nano has a maximum current output of 800mA, I would like to know what is the maximum current output of a STM32 blue pill and black pill. Also, if I plan running a load higher than this current capacity, can I include a buck convertor (with a higher current rating) between the loads and 5V and GND of Arduino but set at the same 5V (or higher), and signaled directly by Arduino pins? Would that work?
Those boards have on-board regulators primarily intended to supply the microcontroller. The Nano has an AMS1117 in an SOT-223 package that can accept a higher voltage than 5V and the GPIO are 5V. Maximum continuous current you can draw from the 5V output with a 12V input will be much less than 800mA because of thermal limitations, maybe 50mA conservatively, somewhat more than that less conservatively. There's also a 3.3V output from the USB-serial chip that is not used for anything.
The black pill/blue pill have 3.3V 32-bit MCUs (STM32F4xx and STM32F10x) rather than the 5V ATmega328P 8-bit MCU of the Nano and they have tiny SOT-23 regulators such as RT9193 that can only accept 5V maximum in and should not be used to supply much additional current from the 3.3V rail, again maybe 50mA or so.
If you need high power (hundreds of mA) you should add an external regulator and external switches. The switches can operate from 0/5V with the Nano, but must be able to operate from 0/3.3V with the other two.