So, because of this post's tangent; I racked my personal memory from my 1980's college days.
I'm just a hack. I've got a little background in math and physics. But I'm a hack at this late stage in life. But I know a little...
As a Civil Engineering Major, the math was there, but the metallurgy... Not so much.
But, as a visual learner, I can be sure that there is friction in any situation where gears are involved. Anytime a linear force goes through a direction change, there is friction. Even the distance of a linear force, such as a long PTO driveshaft, there's power loss through the driveshaft mass, or a a middle bearing carrying the load.
That being said, any, ANY, change of linear projection IS going to produce friction and power loss. Even if it's through a common universal joint or thru a ball bearing (CV) constant velocity joint.
Gears, at any degree of change to the linear, will create friction. The gears in a common automotive Ring and Pinion (90 degrees), and gears in a simpler bevel gear process ( < 90 degrees) in Kubota front axle for example. Is going to produce power loss due to friction.
Every gear system, of any kind, results in the gears sliding against each other at the toe or heel. And usually almost always within the midrange.
Ring and Pinion gears have a machined curve. That's because the force energy can be better distributed across a greater surface area between the pinion gear and the ring gear. Yes .. it's sliding. It's most definitely sliding.
As for the comments about oil viscosity and this application. Folks greater than I have determined through Research and Development ( R & D) what type of oil works.
My hat is off to each of you. Especially those who researched or found in their memories the formulas quoted.