> 2. Productivity in this case means economic output, not the colloquial definition that means "hard work".

The colloquial definition doesn't mean “hard work”, it also means you “produce” more (optionally, for the same amount of time). The difference is how you measure what's being “produced”.

With the “economic output” definition a barista in a posh bar in SF is “more productive” than their counterpart in a popular place in rural Minnesota, because it generates more revenue, even if the later serves twice as many patrons while also keeping the restroom clean (which would colloquially make the later “more productive”).

“Economic output productivity” can also decline if consumer spending do so, not because workers are “less productive” (in the colloquial sense), but because unsold goods or services don't count as “economic output”.

(IMHO overloading things that have a well-defined colloquial term is a very bad habit of economists and it makes things needlessly confusing for laypersons)