Screenshot of the VS Code Extension setting

I have also been confused on this issue for a while. Literally just until a moment ago, I found the answer: There is a setting called "Notebook: Kernel Enabled" and it is defaulted NOT CHEKED!

Mark that checkbox and restart VS Code, open your .vsnb file and there should be pop up message says the Wolfram Kernel has been launched (given the path is properly set or can be auto-detected).