I would like to put up a privacy fence with the framing boards running through the center of the 4x4 post to give it the same look on both sides and the 4x4 looking like a collume between each section

Drill, hammer and chisel will work. Heavy duty Jigsaw may work,
It is a lot of material for a Multi Tool.
Heavy duty Router?

Mortising chisel in a drill press is the only practical way do that.
And even that will be a lot of work.

The holes u make will probably only go half through 4x4 and be of different heights so fence can conform to landscape.

Depending on the land layout, over a 100 feet land may rise or drop 4 feet or more and not be seen by naked eye.

Chuck