How much damage am I actually doing by shifting while pedalling hard?

There are three separate costs and they are worth separating, because they have very different severities.

Immediate risk. This is the real one. Shifting the front under heavy load can drop the chain, and if you are standing and pushing on a climb, a dropped chain means your foot goes to the floor with nothing under it. People fall this way. A dropped chain can also wedge between chainring and frame and scar the frame, which on a carbon frame is not a cosmetic problem.

Wear. Real but slow. Shifting works by deliberately letting the chain climb sideways off one sprocket onto another, and doing that under tension grinds the ramps and the chain plates against each other harder. It accelerates wear on cassette, chainrings and chain — measurably over years, not noticeably over months.

Sudden failure. Rare on a well-adjusted modern drivetrain and much less rare on a worn or badly indexed one. A tired chain shifting under load is how bent derailleur hangers and snapped chains usually happen.

So it is mostly the first item. Not slow poison — an occasional acute risk.

One diagnostic worth knowing: if shifting under moderate load feels crunchy or hesitant on your bike, that is usually indexing or a worn chain rather than technique.

A correctly adjusted drivetrain with a chain that is not stretched shifts under reasonable load with a clean click. If yours does not, you will get blamed for the technique when the actual fix is a cable tension adjustment and a chain measurement — both of which take minutes.

The generational part of your question is fair and the answer is yes, considerably.

Modern cassettes and chainrings are designed for shifting under load in a way that older ones were not. The ramps and pins that help the chain climb, the shaped tooth profiles, the stiffer chains — all of it exists so a shift completes quickly rather than grinding while it waits for you to ease off. Electronic shifting goes further, since it can move the derailleur faster and more precisely than a cable ever will.

The practical upshot is that the advice has softened from "never" to "ease off briefly for the front, and do not be brutal about the rear". A momentary reduction in pressure — half a pedal stroke, not a coast — is enough for almost every shift on modern equipment.

What has not changed is the front derailleur under a standing climb. That is still where things go wrong.