Is the demand for Switch in the US this high that it's sold out? There is plenty of stock all over europe.
Yeah US and Japan (up until recently) are essentially sold out. Amazon US shows Switches in stock but they aren't able to be shipped for several weeks, meaning they are not actually in stock, they're just anticipating a new shipment.
Europe is definitely a bit weaker of a market for Nintendo so it makes sense that it's less constrained there.