As it turns out, I had two dotnet directories in C:\Program Files and C:\Program Files (x86) in the PATH environment variable. The SDK was in Program Files, but the Program Files (x86) one had only the runtime - so, when I ran dotnet, it actually executed the one in Program Files (x86).

The fix is simple. Go to Windows Search, then Edit the system environment variables. In the following image, click Environment variables....

In the following image, select Path and click Edit, in the System variables section.

In the following image, select the C:\Program Files (x86)\dotnet directory and click Delete. (I've already removed it earlier, so it doesn't appear in the following image, but you should be able to find it.)

Click OK on all 3 windows or close them.