I'm entirely clueless as to how to measure productivity at scale in a standardised manner. For example, washing machines create a lot of extra leisure, because

I'm entirely clueless as to how to measure productivity at scale in a standardised manner. For example, washing machines create a lot of extra leisure, because it makes humans productive. A washing-machine assisted human can was 100x as much clothing in a given minute of operation time. But I have no clue where such a productivity improvement would show up in the data. Of course I can study things like 'how many hours do you spend maintaining your household', and you'd see that dropping decade after decade, despite living in ever larger homes with more functionality (and thus, a larger 'maintenance load'). That's productivity, and stand-alone it can be analysed and concluded as such. But fitting that into the same productivity data as say, the construction of homes per worker in an elegant way? I don't know how you would do that. Nor do I know how you account for completely different units across time and sectors. For example, how do we measure productivity of the pharmaceutical industry? Patents per person? Medicines launched? Number of lives saved by vaccines? A GDP per worked hour is of course a great start. But it leaves a lot out, too. For example, technology that sequences a genome for a penny in a short timespan may indirectly lead to gdp growth, perhaps, but in and of itself that massive cheap boost to a researchers' insight into a genome will not show up as a direct boost to GDP, in fact the opposite. Curious to understand from economists how such challenges are typically handled and what the data says.