So after watching a bunch of tutorials on the King Air 350i, I think the purpose of the propeller axis is actually to control the speed of the propellers to limit sound and make the flight more comfortable. By altering the pitch of the blades, the propeller can push more air at slower speeds, so they make less noise. For this reason, many pilots refer to this lever as the "propeller RPMs" instead. However, this pitch is limited by the engine's torque. The lower the RPMs, the more torque is needed, so the pilot has to keep an eye on the torque gauge and make sure to not exceed the engines' capacity.
I'll keep adding to the comments as I learn new info ๐ ๐ฉ๏ธ