Won't the added purchasing power (production) for the working class likewise create more demand and raise prices, therefore counteracting all that?
It wouldn't be added purchasing power due to rational expectations and the permanent income hypothesis. Essentially, the workers would expect lower current and future wages, which would mean their expected wealth wouldn't increase from the one-time transfer and their spending behavior wouldn't change.

Looks like Say's law is "Supply creates its own demand", and has been rejected since the 40s by Keynesians.

https://krugman.blogs.nytimes.com/20...ts-own-supply/
Krugman is not refuting Say's law, but refuting one way that economists have used Say's law to interpret other things. Classical economists didn't have a working conceptualization of aggregate demand (at least not one that works when central banks exist). Many classical economists ended up being wrong about some things because of this. The great Keynesian innovation is the conceptualization of aggregate demand.* Also Krugman's characterization of Say's law is the same kind of Keynesian-specific mischaracterization of it that began with Keynes. To lots of economists, Say's law implied something about aggregate demand even though it was not about aggregate demand. It was a simple observation about where wealth comes from. Both classical and Keynesian economists went beyond this observation and blamed it on the law.


*It should be noted that even though this is the great Keynes innovation, it is still wrong about what aggregate demand actually is. One of the great innovations of the school of monetarism fixed that. Contemporary Keynesians are sorta halfway to accepting it now. Essentially, classical economists didn't think aggregate demand could fall for reasons including implications they derived from Say's law (they were wrong), then Keynes came along and pointed out that aggregate demand can fall (he was right), and then monetarists came along and explained WHY aggregate demand falls.