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.