How MCU provides an output to pins
Somewhere in the literature for most processors there will be representative schematics for the pins.  They can be complicated, but usually with a pin set up as an output it boils down to a push-pull CMOS output stage (sometimes open-drain).

Usually this is found in the MCU's user's manual -- the data sheets are usually at a higher level.

The reason for no drop is -- as stated -- because microprocessors these days are CMOS.  I can't think of one that's not.