At scale you can do this in a bunch of interesting ways. For example, you could measure "amount of time between opening a crash log and writing the first character of a new change" across 10,000s of engineers. Yes, each individual data point is highly messy. Alice might start coding as a means of investigation. Bob might like to think about the crash over dinner. Carol might get a really hard bug while David gets a really easy one. But at scale you can see how changes in the tools change this metric.
None of this works to evaluate individuals or even teams. But it can be effective at evaluating tools.
There's lots of stuff you can measure. It's not clear whether any of it is correlated with productivity.
To use your example, a user with an LLM might say "LLM please fix this" as a first line of action, drastically improving this metric, even if it ruins your overall productivity.