So does this effect on its own mean that the yen becomes more expensive compared to the US dollar?
We don't really know how this will play out, and people's guesses for how it will play out are to some degree already priced into the current rate.
Thats not true. It could be the case that the effect of interest rates on exchange rates is obvious to everyone, and therefore it is already priced in.
Interest rates are not an obscure, arcane thing. Lots of people in finance know how they work, and know how they effect various parts of the economy.
https://documentwomen.com/mrs-watanabe
If you can identify a flaw in a government's monetary strategy, you can always do some arbitrage to take advantage of it, and people do that.
[0] https://www.federalreserve.gov/monetarypolicy/files/fomcproj...