I have yet to find a technological solution to this social problem.

Also, I have yet to encounter this problem. For personal events, I sleep during this time. For company events, we always avoid this time.

I encountered it when I was design the scheduling back-office for a LED video wall a few years ago when those became economical for a shop to own and run 24/7.

The customer probably never noticed if I even did it “correctly” or couldn't be bothered if I didn't, but I remember I was bothered by it: (1) ensuring continuity of programming during the gap when it jumps forward (2) solving the ambiguity when it went backwards.

Because obviously they wanted to think in local time.

I have, in the context of time series charts. Lots of back and forth with QA.

You're right that for the most part this is avoided by convention and scheduling time changes at quiet times of day.

A bit contrived but consider you are a maintenance worker in a facility that uses isolated timekeeping devices. "Change the clock on the vault back one hour at 3:00am".