If you power both an RPI and an Arduino, and want to combine them, power both RPI and Arduino separately, and only connect GND (grounds) together.
if you connect a (5V) Arduino to a RPI GPIO pin, you MUST divide the 5V signal with a resistor divider to 3V, as putting 5V on a GPIO pin will instantly destroy your RPI )cause a latch-up in the SOC chip.
If you have damaged the voltage regulator of your PI by making a connection between its 3V3 and 5V signal, you can throw away your RPI, and buy a new one, RPI's PMIC voltage regulator cannot handle that, and is destroyed.
An RPI is NOT a drop in replacement for an Arduino.
and the "the logic to manage the power??" probably exists only in your imagination.
do you care to explain what you mean by "logic to manage the power" ? what is there to manage?