Rotate current selection of Objects .. Each object with a different Random Rotation ... Is this built into Blender? Is such any such simple Object Mode feature/operation built into Blender? If yes what is the mechanism?
It is certainly built in to rotate all the objects by the exact same rotation.
The result might be for example each object has a random rotation about its own origin on the Y axis.  The rotation would be present in the object rotation entries.
Trusted Addons are acceptable if they of age 3 months or greater.
I checked the standard Addons.  I did not recognize anything.  Rotate has a proportional edit property though I did not see an explanation in the Blender documentation.
Please exclude Particles and Pythons Scripts and Modifiers/Constraints/Keyframes and BAN.  I can write Script or use Particles if necessary.
You can do this using proportional edit mode.
If you have some objects in a scene that is already built and you need to do this operation without affecting anything else, first select your objects.

Press / to enter local view.  This will isolate these objects.

Change your tool settings to operate on individual origins, and set proportional edit to random.

You can now select one object and rotate it, with a large enough proportional edit strength, you will begin rotating each object a proportional amount to the rotation of the one you've selected.

Press / again to return to normal view.