Artic in your explanation above " extension " refers to a extension of the handle of the wrench not an inline extension between the socket and the torque measuring head of the wrench. A totally rigid extension between the socket and the wrench head can be considered part of the socket. At 90 lbs ft a reasonable length 1/2" drive extension is effectively totally rigid. Yes there is slop in the socket to stud, socket to extension,extension to torque wrench but once that slop is taken up the assembly is rigid as seen from the torque measuring device in the torque wrench head.
Also your explanation is correct for the force being applied to the extended "handle" but a clicker type torque wrench as is generally used doesn't care whether you apply one finger pressure a mile away or some muscle 6" away as the wrench is measuring what is happening at the socket end of that handle.
Artic in your explanation above " extension " refers to a extension of the handle of the wrench not an inline extension between the socket and the torque measuring head of the wrench. No. In my explanation the "extension" is the piece that attaches to the socket and then to the torque wrench. Who would use a 4 inch extension to lengthen the handle of a 18 inch torque wrench.

as per the example. "Extensions" are placed into sockets to "extend" their reach. "Extensions" are not available to extend the handle length of a torque wrench. In a pinch one could use a hollow pipe as a torque wrench handle extender. I do this occasionally when I use breaker bars.
Take a one inch screw driver and an eight inch screw driver for example. Which one is easier to use? The longer one because it transfers more torque. Same principal applies to using a socket extender.
Further, I have 3 torque wrenches. 12 inches, 18 inches, 24 inches. They all measure and apply the same torque if set at X amount. But they all have different length handles.
Further, socket extension never line up at 90 degrees. Most ppl use cheap Chinese socket kits with sloppy castings so lots of play/movement to and fro which further cause deviations.
I have given the formula for torque wrench deviations, not to be confused with simply levers or BREAKER BARS.
If one uses a SOCKET EXTENSION between the fastener and the torque wrench pivot point, which is commonly done, one will increase torque from desired setting.
If it makes you feel better I will add; IMO.
