By shrinking the balance sheet, the U.S. is essentially selling its own assets, which are now mainly Treasury bonds and MBS (a type of security), which peaked at $446 trillion.
Shrinking the balance sheet means selling Treasuries and MBS, which are eventually withdrawn from the market, thus tightening the Fed‘s balance sheet.
In other words, the effect of raising interest rates is to make the dollar more expensive, while the effect of shrinking the balance sheet is to make the dollar fewer, amplifying the tightening several times over.
Lower global economic forecasts and risk aversion boosted the dollar, with oil prices likely to be hurt by the release of U.S. crude reserves.