Uh, no. Historically, increased productivity doesn't seem to correlate with working less.
Increased productivity does tent to correlate with increasing wages. Even if not perfectly. More wages does give the option to work less, in order to maintain the same standard of living. But also gives the option to work the same and have a higher standard of living.
Now it's true that if you're working a factory job, then the hours are determined by trying to wring the maximum profit out of the expensive machinery - so ideally you'd like to run it close to 24 hours a day, and that means getting the meatsacks to work as long hours as you can get away with. So harder for you to work less.
But there are a lot of people in their 50s doing 3 days a week nowadays, eithe ras part-timers or as contractors - who didn't really exist in the same way 50 years ago. Work has got, and is still getting, a lot more flexible. Which is partly because we've got better legal protection for workers, and partly becuase people are able to afford to work less, becuase they're better off, because wages are higher, because (again partly) of higher productivity.
if you use the increased productivity to start working less, then everyone else who is, instead, using it to increase economic power is going to inflate you into poverty.
This isn't how inflation works. Purely productivity-based wage rises are not inflationary. Inflation is an increasing amount of money trying to chase a fixed amount of resources - or the same amount of money trying to chase decreasing resources. The point about productivity is that you're making more products and services out of the same resources. Hence productivity increases without wage rises will actually cause deflation. So in a perfect model where all companies in an economy have increased productivity by 10% in a year - wages could go up by 10% as well, and there'd be no effect on inflation. Which means everyone could either take a month off work and the economy would stay the same size, or everyone could work the same hours and have 10% more stuff.
The only thing that truly allows people to work less is concerted, collective action (legislation, unionizing, whatever) to decide that the whole society needs to work less.
This is much more true for your un-skilled factory worker. Management can just see them as an interchangeable unit to be used to operate the machinery - and so for ease you'd like to make them work 1 shift, 7 days a week, 52 weeks a year. And I guess, two 12 hour shifts a day keeps all the machines running nicely. That might be the sort of industry where you'd have to legislate to reduce hours.
But the more of their own knowledge and expertise a worker is bringing to the job, the more they get to control things. And the hours they work become their choice. Particularly if you've the option to freelance. But employers are a hell of a lot more enlightened nowadays about using part-timers to fill one role - which is more expensive in management and payroll workload, but also gives the company more flexibility.
Finally, there's a bit of productivity you've missed. Work hours haven't dropped a huge amount recently. But hours spend on domesic chores fell massively since the 60s. Now we can all have hoovers, washing machines, dishwashers, freezers, microwaves etc. So hours spent on leisure have gone up - and with more productivity/economic growth/technological development, that has also increased our leisure options.