[SalesForce] Not able to Authorize an ORG in VS Code

There appear to be two separate issues here:

1. SFDX must be in your PATH environment variable. That is, the full path of the bin subdirectory where the sfdx executable lives. You'll likely need to relaunch your terminal and/or Visual Studio Code to get them to observe any changes you've made to your Windows PATH.
2. You need to quote any file and directory path names that contain spaces when you're manually invoking SFDX (or any other command line tools) in the shell. Note that some tools don't handle spaces well anyway - you may head off issues with other software if you try to avoid spaces in your paths.

When I uninstalled VSCode, then reinstalled and opened the app, it knew to open the project that I had most recently worked on. That told me that uninstalling wasn't really clean. I was dumping the app from the Applications folder, as well as the .vscode/extensions folder, but there had to be more. That search led me to this thread.

I deleted all those files, did a fresh install, reloaded the Salesforce Extension Pack, and now it works!