So an important thing to understand is that central banks don’t set rates “across the curve” — they set the overnight rate. Some central banks engage in yield curve control where they hint at what level of rates they think make sense, but the Federal Reserve doesn’t do this.
So while the Fed and other central banks control the short term rate, the long term rate (10yr) will drive the bulk of fund flows and set the direction on the currency. That’s not to say that tactical trading around changes in short term rates don’t make sense.
How does this feed into inflation?
Interest rates are comprised of various sub factors. They include the real rate of interest (time value of money theoretically), expected inflation, term premia, and credit risk.
If you look at a current 1yr bond and a 10yr bond, the yields on these might be (hypothetically speaking) 1% and 1.7%. Those nominal rates are expressing a view on the aforementioned factors. So if you think inflation is going to get out of control, you would expect US rates to rise. If you think the inflation will go wild in a few years, then you should expect the spread between the 1yr and 10yr to widen.
This is how market participants express their view of inflation. This then drives the value of a currency.
Example:
You have 100k usd and want to invest it in something safe for 2 years. You compare bonds and find that the US is paying 14 basis points on a 2yr while a German bond is paying -69 basis points with the same duration. What do you buy? If you a German or Chinese company with a lot of USD (from trade), do you convert the currency into your own or would you rather hold 2 year treasuries? What does this do to demand for USD vs other peers? Etc.