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This is not duplicate of questions where OP wants to know how to use stretch to as in these questions the OP is okay with the stretching behaviour that the constraint gives.

I have two empties from two tracks of my two-point camera track. I want to be able to connect single bone's head to one empty and tail to the second empty. The bone should have uniform scaling so that the bone grows uniformly/proportionally as the empties get farther apart.

So far I have tried making the bone a child of one empty, then using the Stretch To constraint to make bones tail reach the other empty. However, this constraint, as the name says, stretches the bone which is not the desirable behaviour. I want behaviour similar to one you get when just moving bones around in edit mode – the bone grows, when you move its head and tail apart.

How can this kind of movement be achieved?

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Add a new bone, set it to copy loc and rot of the stretching bone (in world space), and use 3 copies of the same driver to drive its 3 scale values with the Y scale value of the stretching bone (local space).

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